{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 6.3 (Page 9) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAEHCAYAAAC6IG0BAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAIABJREFUeJzs3Xd4VMXXwPHvTe+9954ASehFekcEQREUC2L7oQg2BEGaghRBUQEFRYodAQVeqtSEDgkJkAIJ6b33bLJJdve+fywiIE1JDGU+z8PjJnfuvZNNPJmcO3NGkmUZQRAE4f6h09wdEARBEBqXCOyCIAj3GRHYBUEQ7jMisAuCINxnRGAXBEG4z4jALgiCcJ8RgV0QBOE+IwK7IAjCfUYEduGeJkmSqSRJ8yRJSpEkqUqSpPOSJL36L65zQpKkUVd8vFCSpBWXXr8rSVKmJEmpkiQNbcz+C0JTEIFduGdJkmQNHAW8gX6ABfA/4CNJkl7+h5c7APS44uPuwAFJktoBY4BAYASwRpIk/TvtuyA0JRHYhXvZUqAAeE6W5XRZ6xjwGTDhH17rIJcCuyRJhkB7IBxoBRTJslwry/JZYBZgdLMLSZLkJ0lStSRJr0qSlCZJUqkkSVP+YX8E4V8TgV24J0mS5Ak8C0yX/17wKAXw+oeXPAb4S5JkCXQCEmRZLgEOA10kSVopSZKLLMurZFmuusW1QgFDQA/tSP9lYLYkSdI/7JMg/CsisAv3qv5AlizL0dc55gpkA0iS9LkkSR1udTFZluuAk0BXtCP3A5c+n3Hpc77ARUmSxt5G30KB3bIsfyXLcj1wCtC/zi8gQWgSIrAL9yp7LgXv63gcbWoFoCUQf5vX/DMdczmwA8iyHCvL8kDgGWClJEmBt7hOKPDHFR/7AOm32QdBuGMisAv3qjTAU5Kkq36GJUkaAHQAllz6lLEsy7WSJL0nSdL8a9tf4wDQF+gIHLl0vXl/jtJlWd4GhAEht+hba+DsFR+HALG392UJwp0TgV24V+289N95kiSZSJJkKEnSc8B6YJQsy1mSJDkAlZIkrQVyZVmeIcuy5ibXPA0EARdkWVZc+lwm8KIkScaXrhcCnLvRBSRJMgM8gZgrPh16zceC0KREYBfuSbIsV6Od4hiCNs1RC0wCesmyvOtSsxCgHZAmy/JPt3FNNXCIv9I4AGuBi2gfyJ4C5siynHSTy4Rcul/1FZ8TgV34T0nieY5wP5Ak6Um00x9bybJceulzb6PNw7+IdvbMDUfaTdy3CqCtLMupzXF/4cEjRuzCfUGW5Y3AXCD4ik+HANHAC8AySZLs/ut+SZLkBUhonwkIwn9CjNgFoQlJkvQo8L4sy12buy/Cg0MEdkEQhPuMSMUIgiDcZ/Sa46Z2dnayl5dXc9xaEAThnhUVFVUsy7L9rdo1S2D38vLi9OnTzXFrQRCEe5YkSRm3006kYgRBEO4zIrALgiDcZ0RgFwRBuM80S479ehoaGsjOzkapVDZ3V26bkZERbm5u6OuLDXUEQbh73DWBPTs7G3Nzc7y8vLgX9iOQZZmSkhKys7Px9vZu7u4IgiBcdtekYpRKJba2tvdEUAeQJAlbW9t76i8MQRAeDLcV2CVJWnNpF/eZNziud2kX9/BL/25Vr/pG9/k3pzWbe62/giA8GG6ZipEkaQSgK8vyQ5IkrZUkyf86ZUtDgfWyLE9tkl4KgiDcxVRqDVVKFZXKBioVSmrK8qmuyqWqNJOa7FzqC6upMtChzNwYQ1lm6psfNGl/bifH3hvYeOn1XqA7cG1g7wIMlSSpD9qdYl6VZVl1ZQNJksYB4wA8PDzuoMtNq6CggJEjR3LkyJHm7oogCM1I2aAmr0JJbnkthVVKSqrrKamsRlOaiW5lOpraJOS6dAyqKjCsMsa41gkdKzvyfczJdDSl2NiUEiMLigM7UhJkh1rShtt2ynM09Qj4dgK7KZBz6XUp2o0LrhUJ9JdlOU+SpB+AR4BtVzaQZXkVsAqgQ4cOd2XlsbKyMsaOHYtCobh1Y0EQ7mn1Kg1ZZTVklChIL64hs7SGnPJa8sprUJYX4KBMxV/Kwlk/HckgH42qCrNyXSjzxrDOExMLB8r8LMnwNiTD0pJ0I1eyJA80ki4ApnI1duoSPJQFtK1LxaGuAXddIzp6t2ryr+12Ans1YHzptRnXz8vHXNrlHbTbi/nfSafmbI/nfG7lnVzib1q6WPDBozd/Q3V1ddmwYQPDhw9v1HsLgtB8SqrrSCqs1v4rqCK1SEF6iYLc8lqQNfhIubTRSaGtXjqD9LOpMcgjzURFfoMhugU26JcFYqBpgb6VLbJzHSmt1cTZ2xJn1IJiyQEAQ1mJd0MOw0igm5MLA/zb42Ri0Wxf8+0E9ii06ZeTaDfpTbxOmx8lSZoPxAGPAQsarYf/IQuL5vtGCIJwZ+pUai7mVxOfW8H5vEoS86tIKqymVFF/uY2PYSWDLDN40TiNAP0kDGsTOKuvIdLQiFPlxiRmGuBf2BoLtTf6ljaYWBhT27mMOC8dzltaEa8bQo1kir5cT4icyws2pQzwbEWwlQO6d9FkitsJ7FuBI5IkuQCDgdGSJM2TZfnKGTJzgV/Q7hSzTZbl/XfSqVuNrAVBeLApG9TE51ZyLquc+NxK4nMrSC6sRqXRZnnNDPUIdDLnST+Zh3RTCFSew67kNPWVGUQ2GHJK35R1xuaYFljTLsWYNpUhFFt60mBqgJmLHiqnOjL8K4iytyVapycNkgEWcjU9DCt5zMOegS4hmOp2auZ34cZuGdhlWa6UJKk3MABYLMtyPtfs0i7LchzamTGCIAiNSpZlMkpqOJtVzpnMMs5mlXM+r5IGtTaI25sb0srFgr5BDrSxk2nTcAb7/CNI6UchMZN8XV0OW9oQZmtPiq4H7RLVtE81oZ0yhFz7ABSmKuptdbC0NybHO5VdLnacNOxCkeSIqVzLcIsaxvj60dHKGp27aFR+M7e18lSW5TL+mhkjCILQZDQamYT8KiLSSohILyUirZTiam06xcRAlxBXS17u7kMbdyvaupnjWJ0AyfsheR+cikKWNSSa2xLm5EuYsz25pYV0uSAz9KIKk9o25DiGkueooU6qxN7CDAOXYs74FXPCugNxvIgs6dDeoJxZXjYMc3LDSPeuWcd52+6akgJ3k/Dw8ObugiA8MDQamQv5lRxLLuZUaimR6aVUKrWzpV2tjOnhb08HL2vaulsT4GiGnqYeUsPgwg7YtRtqSgCJdNfW7G49mN0NxeSX5tI5Oo+xyabY5TiT6/wQ6a7uSKpkPIyU2Nq4kOeaRZh3FWEmfcmSPLGVapjobMAYD388jA2b9025QyKwC4Lwn8spr+VoUhFHk0s4nlxMyaUHnD52pgwJdaaTtw0dvWxwszbRnqCshKS9cHQ7JO2DBgUYWpLv15s/rO3YpcjgQlkiAfElPJdoQ2CsCYXWbch170qyTRmm6nSCTOyosvEiy+MEFzwq2af3GGWSLT76NXzh7cAIZycMdO690fn1iMAuCEKTq1OpiUgr5WBCIYcSi0gt1q4VsTc3pFeAPd387Ojub4ejhdFfJ9XXQNzvELMJUg6Auh7MHKkPHcVBe3c2VyRwMj8C41INT6U5MTXaBoog26s/xzq2oF4Zg610hrYWwRRZBXHR8yhnPHzYp/MqtZIpHU3qecvXi362lvddeRAR2AVBaBIFlUrCEgo5mFDI0eRiaurVGOrp0MXHlme7eNLD3w5/B7Org6paBWnh2mCesAPqq8HcBTqNI9mjPZurktieuoPy0oN0qLBlaZwfjqdSKTcyJrXl0+R7mKKui8RFdQoPu7ZkmpdxwfMg591d2an7GtWSOQOt4B3fANpamDTbe9PURGAXBKHRJBdWsyc+nz3x+cRkVwDgYmnE421d6RvkQFdfO4wNdP9+Yn4cnPkJ4n4DRREYWULwCOpbPcYfmio2Jv3GuYht6Eu6PF8eTN9jtujGJFHo5k90j7GUKavQNJzGEQlfxy4kmxZxzn0baZ72/J/uK5RJtvSwgJkBAbQ2v38D+p9EYL9GaWkpUVFRtG3bFjs7u+bujiDc1WRZJjangj3x+fwRl09KkTbF0sbdivceDqRvkAOBjubXT3UoK7WplugfIDcadA0g4GEIfZIit3ZsTNnKxtNzKVWWEmDsyaLSfvjtuUBDxlkKAwaQPuA1qhT5SIp92Mo6BNl1J824kii37RT4GLBFbyz5kgttTWGNvx9drc3+43en+YjAfoWysjKGDh3KkCFDmDRpEgcPHsTe3r65uyUIdxVZlonPrWT7uVx2xOSRU16Lro5EFx8bxnb1YmBLJ5wsjW50MmSd0gbz+C3QUAMOLeHhjyH0KeJqcvnpwk/sOT0btUZNf5uHeC7NBrOt4TRUZJDbbgTpLXpQVVWApNiBjQqC7XuSa1jPcftwJL9cfjMZyQUpmAAjmcX+3gywtbjvcui3IgL7FWJiYvjss8/o0qULZWVlREdHM2jQoObuliDcFZIKqth+LpftMXmkFSvQ05HoGWDP2/396d/CEWtTgxufXF8DsRsh4lsoiAMDMwgZBe3GonFpw+GcI6wJf4uzRWcx1TdljMtjDIvSQb18Gw01SvJ7vUiKcVuqq4rRVfyBsbKYtg4DqDDW47BFNOa+54iw6cE+6RUsdWUW+7rxrIvtXbXM/790dwb23dMgP7Zxr+kUAoM/vmmTXr16AXD48GEiIiKYPXt24/ZBEO4xBZVKtp7JYcuZHBLyq9CR4CFfW17t6cPDwU5YmdwkmAOUpkHkajjzIygrwDEEHl0GwU+g0jdid9pu1m6fR3J5Mq5mrswMfINuR0pRfLqJ+ppayvu/zEXjDlRXlKNfdxAdxUVC7HphYtuLUyZxmHgeI9/VnWU606nBjLEuNkz1ccVa/+4Mbf+VB/urvw5ZltmwYQPW1tZik2rhgVRbr2bv+Xx+j87haFIRGhnaelgxZ1grBoc44WB+gzTLn2QZ0g7ByZVwcQ9IOtByGHR6FTy6oFTXsTV5K9/Ff0dOdQ5+Vn58HDqDdvsyqJj3NZVKJbUDnyfRvBulRQoMpeOoFVH4mLfF1+tlonRTKXX6HT3/Er7Re5E0yZfOFgYsCPSmlZnxzfv2gLg7A/stRtZNSZIkvvrqK2bNmsW2bdt46qmnmq0vgvBfkWWZ0xllbDqdxa7YfKrrVLhaGTOhjx8j2rnhbWd664uoVdq8+fFlkB8DpvbQcwp0eBEsXFCqlGw4/wPr4tZRoiwh1D6UacFv0yosndJ5n1FeXY168LMk2vYmL1OJgRwPDUcwr3egj9c4Uihmp8UBnPwiOWPdi93Sm9jp6/C1vyfDHaweuDz6zdydgb2ZLFq0CGdnZ55//nnKy8uxsrJq7i4JQpMqVdSzOTqbXyOzSC6sxtRAl0dCnBnRzo3O3jbo6NxGsKyr1j4MPbkCKrLALgCGLYfQp0DPkHp1Pb9d+IXVsaspqi2is3NnPmm5EN8j6RS/Mp/iomJ0eg8hLeAJ0i7Woq/KxtDgCKqSUnp4PI4KI3YbncPE5SQ6nvCx7lQKceQ5Zxtm+bpg+YCnXa5HvCNXGDduHE8++SSrV68mODiYgQMHNneXBKHRaTQyJ1JLWB+Ryd74AurVGtp5WLF4ZChDQ50xMbjNsKAo0QbzyG+1+XOPrvDIJ+A/CHR0aNA0sPXiJlbFrCJfkU97x/Ys6vExgedKKXp5DgUZGRi060jRmI+JjW1ATi7B3CqKkrQogp164eM5gij9NLItw3ALiuN3o+EckvrhbaTL5iDvB2r64j8lAvsVrK2t2bdvX3N3QxCaREVNA5uisvjxZAYZJTVYGuvzbBcPRnf0INDJ/PYvVF0Ix5dD5BrtdMUWQ6Hb2+DWAQCNrGFnyna+OvsVOdU5hNqHMrfrXFqXmFE4aSE5Z85g4O+H6v2viEg0pCqqFhvHFIrT96GjdGR40FsUNFSy1ewE9m7HqXO1ZLbOPKow5w0PByZ5OWF8D1Zc/C+JwC4I97n43Ap+PJHB1rM5KBs0dPKyYdKAAAa1csJI/zqrQG+kMk+bPz+9DtR1EDwSek4G+8DLTY7nHufzqM9JKE2ghU0LpvebzkP6QRR98QUZW7aga2uL0dT5nC31JPdEBeY2xZia7qckKY8efiMxa7DnuF4KhZZn8WoRw6+GT3BE6kOwqSGft/Ak5AFYNdoYRGAXhPtQg1rDrtg8fjyRwemMMoz1dXm8rStjunjR0uUfbgFZmQdHP4Oo70Gjgtajoce7YOt7uUliaSKfR33OsdxjuJq5sqjHIga69KH8+x9J/eYdNA0NWLz4Cqnug4k9ko++URmOHnFkxhzE2zaUvgEjSVMXss/iOE7uEei56vKBNJcyrHnH05FJXk7o306+XwBEYBeE+0pFTQO/RGTy/fF08iuVeNqaMHNIC0a1d8fS5B9O31WUwLHPtYuKNCpo8yx0fwdsvC83yVfks/zMcranbMfcwJwpHaYwOmg0deFHSB83jIbsbMz69UP5+OvsP1BGdVo+Lv5lFCZvJz9WwaDgVzCoNiXcIIFi43MEtjzDFoMh/CENxcdYnx9aeNHO8jZm5AhXEYFdEO4D6cUK1h1LY1NUNjX1arr52bJgRDC9Axxub2bLlZSVcOIr7b8GBYSOht5TwdrrryYqJevi1rE2bi0aWcMLrV7g5ZCXMS6qpmDi21SHhWHg54vtl6uJSrEg9bd8LB0kHNyOkxpxkhbu3Qh17EGGsohjFqdwcI3E0l3BR9IHZOPES652zPR1wUTk0v8VEdgF4R4WlVHKN4dS2XehAD0diWGtXXm5u/c/T7cANNRqR+dHP4PaMmgxDPrMAIegy01kWWZfxj6WnF5CriKXQV6DmNR+Es4GdpR89z15K1aAJGE3eTJ5Xv05sCMdjboE3zYVpEb9BrUyj7Z9E71yfY4aXiTdKI6WIRGEGXdio/Qc9gb6/NrCk942/6L/wmUisF9BpVLh4+ODj48PAMuXLyckJKSZeyUIV5NlmfDEIlaGpxCRXoqViT4Tevvx/EOeOFjcYlXo9Wg0EPMrHPgIqnLBrz/0nQkuba9qdrHsIosiFhGRH0GAdQBru6+lo1NHFBERpM4dR31yCmb9+2E07l0O7S6h4HQKzv6GSKpDxIcdp4V3d0KNepCrKOGo1TlMrM7h75/ClzoTiCGYIfaWfBro/sCXA2gM4h28QkxMDE8//TSLFi1q7q4Iwt+o1Bp2xuaxMjyFhPwqXCyN+ODRljzV0f32555fKzUc9s7U1mZyaQdPfAte3a9qUllfyZdnvmRD4gbMDcyZ2XkmTwQ8ARVV5E57n4qtW9F3dcXlq69IUfkSsSoNPUMdWnWr5fzhNahq6hnSaSLGRcacNkwjTh1Pq8Ao0i3NmaHzKbWYstjfjTEutmL1aCO5KwP7oohFJJQmNOo1g2yCmNpp6k3bnDx5kh07dhAWFkZISAjffPMNenp35VskPEDqVGp+i8rmm0OpZJbW4OdgxqejWjO8jQv6/zYHXXgB9s3W7iNq6QFPrIFWI+CKPT9lWWZn2k4+ifyE8rpyngx4koltJ2JhYEHVnr3kf/QR6ooKbP/3P3RGjGXvhjQK01PwbGWGuu4AUTuO4e/diXbe/akoqWKXbQxKvXjah0Txm+4wdvIoQSZGfN3KkyBTUeOlMYmodYWOHTuyf//+y2UFdu3axbBhw5q7W8IDqk6lZmNkFivCU8irUNLazZLpj7RnYEvHf/5A9E+KYjg4D6K/BwNzGPARdBoH+lencNIr0pl3ah6n8k4RYhfC1/2/poVtCxoKC8n56E2q9u3HqFUr3L79lguZxkQsicHASI+2A3SI3b+C2ooKBncdj3m+OclyPsdM4nF3jMHKLZf5OrNJlt15wdWOD3xdxGKjJnBXBvZbjaybSmhoKIaGhgB06NCBpKSkZumH8GBTNqjZEJnFyvAU8iuVtPe0ZvHIULr72f37VIW6QVs+N2yhdqZLp3HQayqY2FzVrE5dx5rYNayOXY2RrhGzusziCf8n0JF0KP99MwWLFiHX1eEwZTLSw6PY+UMihRl5eLe2xkA/ghMbt+PiEsQQv9eoz6vliGMKabUXaNP2NLFGjnyr8zl6ukasDfLgEXtRi6mp3JWBvbmMGTOGGTNmEBwczNatW5k+fXpzd0l4gCgb1PwakcnKQykUVNbR0cuaT0e1ppvfHeaeU8Lgj2lQlAC+fbW7FV2xWvRPJ/NO8tGJj8isyuQR70eY0nEKdsZ2NOTkkDNrNorjxzHp0AHHuXNIyjTg+MfR6Bno8tBjVsQeWENxZjo9ujyDa7knhVVlhNucR0fnIh26nGaD9AS7eITWZsZ828oLD2PDO3inhFsRgf0Ks2fP5plnnkGWZYYNG0b//v2bu0vCA6BBreH3qGyWHkgir0JJJ28bPn+yDQ/53mFAL0uHPTMgYYd2Dvro9RA4GK65ZmV9JUtOL2Fz0mY8zD1YNWAVD7k8hCzLlP/+OwULFoIs4/ThB+gPHM6+nxLJPF+Ke0tr7FySOfzjz5iYWjGyz3R00lXE2+VxsiYOf/cL6Dqms0B3NokaT152tWO2nwuGOiL10tREYL9CcHAwMTExzd0N4QGh0chsj8nl830XSS+poa2HFUtGtaar3x1uot6ghGNfwJHPQEcX+s2GLhP+lkcHOJB5gPkn51OqLOXl4Jd5rfVrGOkZ0VBYSP7sD6gOD8ekUyecFywgs0Cf8PmRqOs1dBnuRPqZXzmxKZrgNv0I0e1GbUY1x5zTyFIk0rFTFBcMrPhaZxkayZhvWrkz3MH6zr4u4baJwC4I/zFZltl/oZAlexNJyK8iyMmc1c93oF8Lhzuf7pdyEHa+C6Wp2lkuA+eBpevfmhXXFrPw1EL2Zuwl0DqQ5f2W08q2FQCVu3aRP2cuGqUSx+nvY/rEaA5vTCbxVD4Onua06Kri6C8LUSqqGTroLUxTjCk0LuOgTRw6pNC5yyk2S0PYwuO0MDHm22AvfE3+xfx64V8TgV0Q/kOR6aUs3HWB6MxyvO1MWfZ0W4aGOP/7WS5/qsyDPdMhfjPY+MCYLdp8+jVkWWZH6g4WRS6ipqGGN9u+yQvBL6Cvo4+qrIyCjz6ictdujEJDcfl4IWWSLTsXnqaqtI72g92pqz7KnpWbcXDxZlj7t1BfrCHBuYjjFTH4OCdh7hLPEt2pnNEEMdrJhoUBbmLWSzMQgV0Q/gMpRdUs2p3A3vMFOJgbsnBECCPbu/37eeh/0qi1s10OfATqeuj9vrY2+nXSLsW1xcw9MZewrDDa2LdhTrc5+FhqV1krjh8nd9r7qMrKsH/7LWxeepkzB3OI2BaNqZUhA15yJ3LrSvKSEunYbTj+ta2pTa/iuHs6aaVJdOhwjlyjOj7VXUapbM6nge4862wjFhw1ExHYBaEJFVXVsfTARdZHZGGsr8vkgQG81N37368UvVJ+LGx7A3LPaEfnj3x6VSndK+1J38O8k/OoaahhcofJPNfiOXR1dNHU11P0+ReUrluHgY8P3l+vRO3iy/YVcWQnlOHbzgGPFmXs+WoGsiwzfPh7GJ3XocSokgO2cTTUptGtewSHCOE76TVs9Q3ZGuxFOwtRkbE53dZPlyRJa4CWwE5ZlufdpJ0j8Icsy21v1EYQHgS19WpWHU7lm8Mp1Ks0PNfZgzf6+WNn1gjT/BqUcHgxHFsKxtbaVaPBT/xttgtAubKcBacWsDt9N8G2wczvPh8fK+0ovS45mZzJU6hLSMDq6dE4vvcemckKDsyLQFWvptczfhSl/sHuL7fh4hNEn8DnUMVUke5aSXhFNC7WGbh6n2Sdzjj2aXrQ3dKMr1t5YdcYv7SEO3LL74AkSSMAXVmWH5Ikaa0kSf6yLN9o5c6nwD27NnjlypVs2LABgPLycjp37sw333zTzL0S7iWyLLPtXC4f704gr0LJ4GAn3ns4CG+7RhrBph+F7W9BSbK2PvrAeX9bZPSnQ1mH+PDEh5TXlfNG2zd4Kfgl9HT0kGWZsvXrKVy0GB0TE9xWrMCkZy+Ob0nh3IEsbN3M6DrCkaM/LyUvOZHOfZ/AtzqYusQKon3yicmLo3XrizRYpLJAdxGJahcmejgwzdsZPbEZxl3hdn619gY2Xnq9F+gO/C2wS5LUF1AA+Y3Vuf/a+PHjGT9+PABvvPEGY8eObeYeCfeSs1nlzNkez5nMckJcLVn2dFs6el0/6P5jygptbZeo78DKE8ZsBd8+121a01DD4sjF/J70OwHWAazsv5IgG23pXVVZGXnvT6c6PBzT7t1xWbiAGsmMzZ9GU5heSUhvN5x9y9i+ZBoatYrHnpyK0TkdqvQVhLsmUFScSrduZ7moo8+Xul9ShzFrgj0YIlaR3lVuJ7CbAjmXXpcC7a5tIEmSATALeBzYer2LSJI0DhgH4OHhcdMb5i9YQN2Fxi0CZtgiCKfbXEmak5NDQUEBHTp0aNQ+CPen/Aoli/9IYPOZHOzNDVk8MpSR7dzufKbLny7uhe1vQnUBdH1D+4DU4Pp/AcQWxTLtyDSyqrJ4KfglJraZiL6uduckRUQEuZOnoC4rw3H6+1g/9xzpsSUc+D4SWSMz4OUWFCTtYdunv+Hg6cOA9q+giqyg0LmWfcpojDQ5PPTQcfbRjR8Zi4ehEetCvAk0FVMZ7za3E9ir+Su9YgZc7zH+NGCFLMvlN3oKLsvyKmAVQIcOHeR/3tX/zldffXV55C4IN1KnUrP6SBpfHkxGLcu83tuX1/v4YWbYSDnm2nLtFMazP4NDSxj9C7j+bVwFgEqjYk3sGlaeW4m9iT1rBq2ho1NHAGS1muKvv6b4qxUYuLvj/vVK9AODOL45hbP7s7D3MKfHU64c/mkp2efjaNdrKC2lLtSfKSfJt4IjuVH4+eVg63KCNboTOaDuQj8bC1a09MBS1E6/K93OdyUKbfrlJNAaSLxOm/5AX0mSJgBtJElaLcvyK/+2U7c7sm4KGo2GsLAw5s+f32x9EO5+hy4W8eG2eNKKFQxq5cjMIS1xtzFpvBsk7dfOeKkugB6Todd7oHf9B6/ZVdlMPzqdM4VnGOw9mJldZmJhoN2BqKGgkNwpU6iJiMBi2KM4zf6Amnpddi6JJj+k5XnDAAAgAElEQVS1kuBerniHNrDtk2koFQqGjJ6ExXkTlMpKTvplkZCTQIcOiSiM01io+ymJaife8XRkircTOmIq413rdgL7VuCIJEkuwGBgtCRJ82RZnvlnA1mWe/75WpKk8DsJ6s3tyJEjdO7cWcy/Fa4ru6yGj3acZ098Ad52pnz/Uid6Bdg33g2UFdpR+pmfwD4IRv98w1E6wPaU7cw/NR8JiYU9FjLUZ+jlY9WHD5M7dRoapRLnhQuxevwxMuNL2Lf2PGq1hgEvt0RREsnv81djYefAk0Mmoz5RSbVVHfst4igvzKBHzzMkyAYin36PuWVgl2W5UpKk3sAAYLEsy/nAuZu0791ovWsGe/bsoWfPnrduKDxQlA1qvj2cylfhyUhITBkUyCs9vDHU0228m6SEwf9NgKo86D4Jek+74Si9pqGG+afmsy1lG+0c2rGgxwJczbSlA2SViqKlSyn5djWGgYG4fv4ZBl7eROxII3JnGrYupvQb60/k/63lwtFwfNt1oZvbY9QdK6PQq4G95RGYSQU81PUIB+jKd9KLuBsa8l2Ij8in3yNuK0Emy3IZf82Mua8tWLCgubsg3GWOJxczY2scacUKBgc7MXNoS1ytGnFWb0Mt7P8QTn0NdgHw8n5wa3/D5udLzvPe4ffIqsritdav8Wroq+jpaP9XbigoJOfdSdSejsLqySdxnP4+9Spddnx1jsz4UgI7O9G6nzm7ls2iODuTno+9gEeRD8q4UhKDKjmWEYWfXx72Lof5TmcCe9Td6GNjzsqWnliJfPo9Q3ynBOEGSqrrmL/zApvP5OBpa8IPL3WiZ2OmXUC7anTzq1CcCJ1fg/4fgv71f2nIsszPF37ms6jPsDayZvXA1ZcfkAIoTpwgZ/IUNDU1uHyyGMtHH6UgvZI/VsVSU1lPr2cCMTbJ5tfZH6Kjp8fIF2ejf0pFraaak/5ZJGYk0KFjCnVGF1is9wlxKlded3dghq8zuiI1eU8RgV0QrqHRyGyKymLh7gQUdSom9vFjYl8/jPQbMe2iVsGxzyH8YzB1uGHRrj+VKcuYdWwWh7IP0dutN3O7zcXaSFsGV9ZotLNeln+JgY8Pnt9/h4GvL/FHcji84SImFgY8PqktadG72bPpZxy8fXm413jqwouotoX9RnGU5WXQo2cMqXIDy/RWUKkxYUVLD0Y4ilK79yIR2AXhCkkFVczYEkdEeikdvaxZ8HgI/o7mjXuT0lTtKD07QlsKYMgSbWmAG4guiGbK4SmUKcuY1mkazwQ9c/nhvqqsjNwp76E4ehSLRx/F+cMP0BgYcfDHBBKO5+He0oZeT3sR9t2XpJw+Savu/elgOxDloSJKfNTsKYvAUF1At+7HOKoJ5ludCdjpGbAtxJtQ80ac5SP8p0RgFwSgXqVhZXgKX4YlYWKgx6InQhjV3r3xFhkByDKc+xV2TdZugPHEGggZecPmGlnDurh1LD+zHFczV35+5Gda2La4fLw2Jobst95GXVKC05w5WD05iuqyOv5YFk1hRhUdHvHCt60evy+YRnl+Lv1Gv4Zzlgu1scWkBtcQnnIKb+8iXNzD+JUX2MoAuliY8m2wF/YG+o33dQv/ORHYhQfeuaxy3vsthsSCKoa1dmH2oy0bp1jXlZQVsGMSxP0Gnt1gxCqwdLth83JlOTOOzeBw9mEGeg5kTtc5mBmYAdpce/mGjRTMn4+evT2ev/yCcXArshPL2PNtHGqVhsGvhaBpSGH9rCXo6hswatwcdI/WUaeuITIon9jkONq1z0QyjeILvbmcVvnyvIst8/xdMRBb193zRGC/JC0tjYkTJ1JZWUmnTp1YsmRJc3dJaGK19Wo+25fImqNpOJgbsfr5DvRv6dj4N8qKgN9fhooc6DtTO5VR58b5+rOFZ5lyeAoltSVM7zyd0YGjL6deNEol+XPmUrFli7bWyyeL0bWy4uz+TI5vTsHKwZiHx7Ui4dg2Tvy2Hicffwb1G49yXyG11nDQ7Dz5men06BlPLqUs019BntqcRQFujHW9wy35hLuGCOyXTJ06lVmzZtGlSxeeeuopwsPD6d27d3N3S2giJ1JKmLY5hoySGp7p7MG0wUFYGDVy+kGjhiNLtA9ILd3gpT3g3vGGzWVZ5ofzP/BF1Bc4mjry4+AfaWXX6vLx+uxsst94k7oLF7B7/XXsJryOSg371p4nKbIAn7b29HjSiwNrlpIceZLgnv3p4PAwtfsLqPCGP6oioKaAHj1PEq1xYYXOFxhIBmxq481DVmaN+7ULzequDOxHNl6kOKu6Ua9p525GjycDbnj84sWLtGunXeHn4OBARUVFo95fuDso6lQs3H2Bn05m4mlrwvr/deEhX9vGv1FFDvz+CmQeh5BR2gekRpY3bF5VX8WsY7M4kHmAvu59+aj7R5fLAoB2FWnOlPdAlnFbuQLzPn2oLK5l19exlORU0+UxH7xb6/PbvKmU5mbT95lXcc11pzaqiOzgevalHcfFpQRvn4Ps4FF+ZiStTExYF+KNu5FB43/9QrO6KwN7cxg5ciRz5syhS5cu/PHHHyxcuLC5uyQ0spOpJUz57RzZZbW83N2byQMDMTZoxCmMf7q4B7a8Bqo6ePwbaD36ps2TypJ4J/wdsquymdxhMs+3fP5y6kXWaChZtYqipcswDAzEbdlSDDw8yE4oZc+38ciyzNCJrZFVGfwyYxGSpMPI1z5E/3gDdTXVxISUEJl0hpCQPEysj/KN7lQOqVszzMGKz4PcMdVtgq9faHZ3ZWC/2ci6qcycOZOjR4/yySefMHbsWMzMxJ+m94vaejWL9ySw7lg6nrYmbHz1ocark34ldQMcmAPHl4NjCIz6Duz8bnrKztSdzDkxB1N9U9YMWkN7x79WnKqrFeS9P42qffuxGDoU54/mIhkZce5AFsd+T8bK0YTBrwWTErGHwz9/h527B488+hbKvYXUmcJhr2TSU5Lp2vUi5XrpLNBfRrLKjuk+zrzh4SDqId3H7srA3lzatGlDZmYm69evb+6uCI0kKqOUyZtiSCtWMPYhT6YODmqc/UavVZYBv70EOaeh4yswcP51N5T+U4O6gU9Of8L6hPW0c2jHp70+xd7kr1WtdWlpZE98g/r0dBymTcVm7FjUKg2Hvr9Awsl8vFvb0ftZX8J/+JoLR8II6NSNboEjqdmVj8JNYo86mpqiHHr2iua82oDlul/SIBvxfYgnA+1unBIS7g8isF/hk08+YdKkSZiYiIUZ97o6lZrP9yWx6nAKzpbG/PJKZ7r6NdGsjwvbtcW7ZFk7Sm/1+E2b5yvyeffQu8QUxTC25Vjeav8W+jp/PbitCg8nd8p7SHp6eKxZjWmXLlSXKdn9dSyFGVV0HOpNUBdztnw8k/yUJLo/MQYfRStqjuZTFKTmj7wTWFgU0eWhwxyQu7JOR1vE6/sQHwJEEa8HggjsV5gzZ05zd0FoBBcLqnjr17NcyKvk6U7uzBjSsvE2v7iSql67Xd2pleDSFkauAxvvm54SmR/J5EOTUaqULOm1hIFeAy8fkzUaSr75hqJlyzFsEYT78uXou7qSn1rBrq9jUdWpGfxaCMampfwycxL1tbU89toMTM/ooywuIym0msMXTxEQUISdczjfS6+xW9NDFPF6AInvtHDf0Ghk1h1PZ9EfCZgb6jXdvHSAimzY9AJkR0KnV7WbSuvdeHbJnwW8Pj39Ke7m7qwbtA4fK5+/+q5QkDvtfar27cNi2KM4z52LjpERF47nEv5LImbWRgx/uw35SafY9umXmFnb8PiY6aj2l1GPklOBOZxPOk+Hjqk0GMfzie7HxKrdRRGvB5QI7MJ9Ib9CyeRN5ziaXEy/IAc+fiIUe/NGXj36p+T98Pv/QF1/W6mXWlUtc07MYWfqTvq692V+9/mXV5EC1Gdlkf36BOpSUi7n02WNzNGNSZw7mIVbkDUDXm5BxNafidqxBfeWofTv8TI1O3NR2kocNImnMCudHj1iSUPJMr2vqJBN+bKFOyOdmuAhsXDXE4FduOftiMllxpY46lUaFjwewtOd3JtmxodGDYcWw6FF4NACnvwB7Pxvekp2VTbvhL9DYmkiE9tM5H+h/0NH+mvJvuLECXLefgcZ8Fj9LaZdu6JUNLB3dRxZF8oI7etG+4ed2P3lQtLPRtF2wKO0tuxNzd5cyn3gj8qT6Cjz6N7jBEc1LVgtTcBGz5D/C/GmtSji9cASgV24ZynqVHy4LZ5NUdm0cbfi86fa4G1n2kQ3K9YuOEoNg9ZPw5DPwODmgfN47nHeO/weGo2GL/t9SU+3v3bmkmWZsh9/omDRIgx9vHH76isMPDwozVOwa0UMVaVK+owJwslb5tcP3qOiII+BYyfimOFMbVQhWcF17E87gatrIZ7e4aznOf6PQXS2MGW1KOL1wBOBXbgnxeVU8Ob6M6SVKJjYx4+3+vujr9tExauyo2DjGG1wf3QZtHsebvIXgSzLfB//PZ9Hf46PpQ9L+yzFw8Lj8nFNfT35H86hYvNmzPr3w+XjReiamZIeW8zeNfHo6evw2DttqVOk8svMRejo6DLq9TnoHqmnrqaSc8HFnE4+S2jrDPQso1mi+wHRaj/GutjykSjiJQDiJ+AaBQUF9OjR4/LHFy5cYPjw4c3YI+FKsiyz5mgaI1YcR1Gv4udXOjN5UGDTBfWo72Ddw9qiXS/vhfZjbxrUlSol7x99nyVRS+jn0Y+fH/n5qqCuKioic8zzVGzejN2ECbgtW4aOqQnRezPYuSIGS3tjRk7rQN7FQ2xe+CHmtvY8+cJcpD0K6uR6wjxTOJN2mq7dzlFlmc4cvS+J1fjxSaAbiwLdRVAXADFiv0pZWRljx45FoVAAkJKSwpQpU6iubty6NcK/U1xdx+RN5whPLKJ/C0cWjwzFxrSJ6pw0KLV108/8CL794InVYHLzB5H5inzeCnuL8yXnmdhmIuNCx12V66+Njyd7wkTUFRW4Ll2KxaCBqBrUhP+UQOKpfHzbOdD7WT8O/biKuLC9+LbvQs+Q0dTsyEPhKrFHE42yNJPuPSI5JXvwjTQLc11Dfg/1opMo4iVc4a4M7GHfraIwI7VRr+ng6UOfF8bdtI2uri4bNmy4PEI3Nzfn999/Z9CgQY3aF+GfO5ZczFu/nqVS2cDc4a0Y08Wz6ZbEl2fCxue1+5H2nAK9379pmV3Q7nL0Tvg71KnrWNZnGX08+lx1vHLXLnKnz0DXxhqvX37GqEULFBV17P46loK0Sjo96k3L7tZsXfwBOQnxdBk2mkB1W2oO5VEQoGJvwUmsbfJoFXqYDYxiK0Nob27CmmBvnAxFPl242l0Z2JuLhYXFVR87ODg0U0+EP6k1MssOJLHsYBI+dqb8+HInWjhb3PrEfyslTFsaQKOC0esh6JFbnrLp4iYWnFqAq5kr6/pcPT9d1mgoWr6ckpVfY9yuHW7Ll6Fna0tRZhW7VsagVDTw8LhgLGwV/DJjEjXl5Qx9ZQpW8WbUFpSQ2KqKoykRBLXIxsQ+is903idKE8izzjYsCHDDUKRehOu4KwP7rUbWwoOhsErJ27+e5XhKCSPauvLRY8GYNsUKUtCWAzi+HPZ/APZB8NRPYOt701MaNA0siljEhsQNdHPtxuKei68qtatddKQt4mX5xAicPvgAHQMDkqMKOfDdeYzM9BkxpT3l+XGsn7UEQ1NTnnztI+SwSmrVNZzyzyYx7TydO1+gwLCExbpLKZIt+STQjTEuYlMM4cbuysAuCMeTi3nz17NU1zWweGQoo9q7NV3qpb4Gtr8JsZug5XAYvgIMb56zLleW8+6hd4nIj+CFVi/wdru30b0iXdOQk0PW6xOoS0rC8f1pWD//PMgQsSONyB1pOPlY8PCrIcQe2MqxDT/i5BfAw/1fp3ZXPrXWGvYbx1FekEr3HlGclN34Vmc65nqGbA72pqNlE03pFO4bIrALdxW1Rmb5wSSWHtCmXn5+pTOBTuZNd8PyTPj1WciPhX6ztdvW3eIXSHJZMm8cfIOCmgLmd5/PMN9hVx2viY4me+IbyA0NuH/zDWY9utNQr+bAdxdIiS4ksIsT3Ud6s3/NUhKPH6ZF9750dhlC7Z48SjxV7KmMxFTKpGOXE6yXRrKdwXQ0124yLfLpwu0Qgf06wsPDb/qx0DRKqut469ezHE0u5vG2rsxrytQLQNoR2DQW1Cp4ZiMEDLzlKYeyDjH1yFSMdI1Y9/A6Wtu3vup4+Zat5M+ejZ6LM+4rV2Lo40N1mZJdK2Mpyqqi6wg/fNub8Nv89ylIS6HXqBfxKPGjJrKA1CAFhzIj8PVLx9gphkU604nV+PKiqx1z/FzEVEbhtonALtwVzmSW8frP0ZQo6ln0RAhPdmiisgCgzadHrII/3tfm0Uevv+WGGLIsszZuLUujlxJkE8SyvstwMnX667haTeFnn1G6Zi0mXbrg9sXn6FpZkZ9Wwe6VsTTUqRkyPhRD4xJ+mT6DeqWSx/83HeNIXWqrKzkdkEd8Zizt2seTa1zDQt2lVGHO0iB3nnIW9V6Ef0YEdqFZybLMTyczmLvjPI4WRmwe35Vg1ybcCEJVBzsnwZmfIPAR7dZ1RjefZVOnruPD4x+yI3UHD3s9zNxuczHWM758XF2tIHfKFKrDwrB6ejRO06cj6etzMSKfgz8kYGplwLC32lCQGsnWxcu0lRlHv4/qYBnVRvWEOydQUniRbt1PE0YQ30uv4mRgxPpgL0JEvRfhXxCBXWg2tfVqpm+JZcuZHPoE2vP5U22wMmnCjZWrC2HDc5B16tL89Olwi/RGcW0xb4e9zbmic0xoM4FXQ1+96i+J+uwcssePpy41FcdZM7F59llkjczJ/0shancGLv5WDPxfC05vW8/p7ZtxbxFCvw4vUrungFLnBvbWR2FEKm06R7Jaep4wuSe9rc1Z0coTG1E/XfiXxE+O0CzSihWM/ymKxIIqJg0IYGIfP3R0mrBmeN45WP8M1JRoN8QIHnHLUxJLE3nj4BuUKcv4rPdnDPAccNXxyw9JVSrcV32DWbdu1CtVHPjuAqlni2jRzZkuw93Zs3IxqdGRtO03lBDD7tQeLSDVp4rw/Ej8/JKQnFKZqzOXVI0Lb3k68p63k6ifLtwREdhvIS8vj/j4eDp37oy5eRPOzniAHLhQwNu/nkVXV+K7FzvRK8D+1ifdifgtsGW8tiTAS3+AS5tbnhKWGcbUI1MxNzDn+8Hf09K25VXHy7duJX/WbPRdXHBbuRJDH2+qSpXsXBFDaU413Uf5495Shw0fTqE8P5cBT0/AIdWBmvQSov3yics7R7v2Z0kwNuVrnc/R1THmh1ZiP1KhcTTaY3ZJkmwkSRogSdI9vXLiyiJgFy9e5KmnnuLYsWP06tWL+vr6Zu7dvU1zaRXpy9+fxsPWhB1vdG/aoK7RQNgC7U5HzqEwLvyWQf3Ph6Rvhb2Fr6Uv64esvyqoyxoNhUs+I2/a+xi3a4fXhl8x9PEmP7WCTR+fpqq4liETWmPlUML6Ge9SU1HOEy/MxvasFVVVlex1TeBiyUk6dz3ETuN2fCrNwMvUkr0dAkVQFxrNbY3YJUlaA7QEdsqyPO86x62BHcBO4DNJkvrKslzUqD39D1xbBCwmJoZ169bh6+tLbGwsaWlpBAYGNnMv703VdSombTjL3vMFPN7WlYUjQjDSv3n9lTtSr4Atr2o3mm7zHAz9DPRuvqNSvbqeOSfmsC1lGw97PcxH3T7CSO+vzZ81CgU5U6dSvf8AVk8+idOsmUj6+iSezOPgTwmXt6/LOHeQ8B9WY+PixiN936A+rJgiWyX7NWcx1U0gsFMcn0pvESO3ZLSTDQsD3DBuquqUwgPploFdkqQRgK4syw9JkrRWkiR/WZaTrmkWCkySZfnkpSDfDtjzbztVvj2F+lzFvz39ugxcTLF69OZLxK8tAjZy5EhUKhU7d+6krKwMP7+bT4kTri+tWMG4H06TWqxg1tCWvNTNq+mmMgJU5MCvT2sXHQ2cDw9NuOWiozJlGW+HvU10YTTjW49nfOvxV/WxIS+PrPGvU3fxIo7T38d6zBiQ4cSWFKL3ZOAaYMWAF4M4umE1cWF78Wvfla6uw1EeKSLFvYIjpVEEBMZSZlfDTOkTKrFgSaA7zzjbNO17ITyQbmfE3hvYeOn1XqA7cFVgl2X5EIAkST2BTsDcay8iSdI4YByAh4fHtYfvCtcWAQOorq5m48aNeHo2YTXB+1hYQiFv/noGPR2JH1/qRFe/Js7U5URpH5LWK+DpXyHg1pU5U8tTmXBgAoU1hSzuuZjB3oOvOl4bE0PWhAnINbW4f70Ss549qVeq2Lf2POkxxbTq4UK7wfZs+/xDchPP023oM3iXBaGIKyLSM4eLZedo3zGSgwahrJfG4mpoyM/BYus6oencTmA3BXIuvS5FOxr/G0kb9Z4CyoCGa4/LsrwKWAXQoUMH+WY3vNXI+r9kZWXF999/z5gxY4iMjKRz587N3aV7gizLrDyUwid7EmnhZME3Y9rjbtPEgSx+C2x5DcwcYMwWcGx5y1OO5x5ncvhk9HX1Wfvw2r+tJK3YuZO86TPQs7fHfe1aDP39qSyuZeeKGMrya+g5OgB7j1p+nTmZ2qpKhj07FdNzepSrygh3vohCGUNol3N8Lb1ABJ0YbGfJF0HuWIqpjEITup3EXjXw52oMsxudI2tNAGKAYddrc68ZP348hw8fBqC8vBwrK6tm7tG9Qdmg5p0NZ1n8RyJDQpz5fXzXpg3qsqzdZHrTC+DcBl45eFtBfWPiRl7f/zpOZk6sH7L+qqAuyzJFX35F7ruTMQoOxmvjBgz9/clNKmfTx6dRlNfx6ButMTBMY8MH0wAYNWo2xich16CcrcaRGJgfxrJ1MjN15hItdeJDXxfWBnuJoC40udv5CYtCm345CbQGEq9tIEnSVCBPluUfACugvDE72Vzee+89xowZgyRJDBw4UDw4vQ2FlUr+92MU57LKmTwwgAl9/Jo2hdWghG0TtZUZQ0fDsGW3fEiq1qj59PSn/HThJ3q69WRxz8WY6v9VMVGjVJI3fQaVu3Zh+dhjOM2dg46BAeeP5XLol0Qs7IwZ/Fow8eG/E7F1E+6BwfT2f5a642XEOxdxuiqaVsGnOW3hzQ/Su9jqG7K5lbfY5Uj4z9xOYN8KHJEkyQUYDIyWJGmeLMszr2izCtgoSdIrQBzaXPw968+iX97e3hw9erR5O3MPic2u4H8/nKZS2cDXz7Xn4WCnW590JxTFsP5pyI647cqMigYF7x1+j8PZhxnTcgzvtn/3qnK7qqIisiZORHkuBvt3J2H7yivIGpmjm5I4dyAL95Y29H7Gi/2rPyXtzGna9XqUlqqOVMcXc8wljfy6s4R0juY73dGckLrTy9qMr1p6YWcgRunCf+eWP22yLFdKktQbGAAslmU5Hzh3TZuyS8eFB9TOmDze3XQWW1NDfnutKy1dmnCXI4CiRPh5FFQXwKjv+f/27jsqiusL4Ph36AKCgCAiYgNERRHFisYea4wx9l4SY40lGjX2mljzM7F3Yy+x94YVKwhYUYiI9CK9szu/P9aYaFRQWer7nMM5JPNm976zcB1m7ruPap2yPCUsKYwR50bgH+vPtPrT6Fa522vHUx894vmw4ShiYynz+28YtWpFWnIGp9ffJ/DBC2o0s6ZKQz32zZtEXHgobTqPwuSxERGZkZwveR89XU9MHaOYIU0nAnMmVyjNqHIWaIiH7kIuy9ZlxMvEvSfLgUKRI8sy/zur6p/uUs6E1X1rU9Lw/bdCPpm/G+zpr7rlMuA4WNfO8pT7UfcZeX4kqZmprGyxkoZlGr52POH8eYLHT0CzeHHKbdtKsWrViA1P5thKH+KjUmjWxwE9g2B2TpuKprY2Xb+aBp4p+JeI4IrmHSqWu8Edswpsl8ZgpqO69VJf3HoR8oj4+1D4aKkZCn7c58Nh7xC61LZm3leO6GqpcdERgMdmODoOzCtDr91QIuvS2bPPzjL58mRM9UxZ13Ydtib/rEeQZZkXGzcSsXgJetWqYb1iBdqlLHj+4AWn1t9D0pDoONqJoAfnOLH8D0qXs6O5Qz/SPOK4XSoQv3RP7GvdYYtOd25KDWhuasjvVcpjJm69CHlI/PQJHyU6MY0hWz3weBbDj20qM6xJJfU+JFUqVfuRuv8Gti1VjbyyaLcryzKb7m/iV49fqWFeg2XNllGy2D919HJ6OqEzZxG3fz/F27bBav58JD09vM8/5+o+P0xL69NqoB3ue9fy+PoVqtf9nOpSQ2IeR3DR/DEK3ZuY1IhmtsZPRGHO1IqlGW4jbr0IeU8kduGD+UUkMHDzLSLi01jRqxbta5RW7xumJ8OBIar2AC6Doe1C0Hz/j26GMoO51+ey/8n+t7YHyIyJIXjU9yTfvk3J4cMpOXIESiVc3PaIB1dDqeBUkjrtTTm6bDrRzwNp1W4oZk9NCZRCuGjsQ5ky7nhYVGa3NJpSOtocdKwk9iIV8g2R2N8QHh5Oly5duHz5MsHBwdSrV+9VK4G9e/dibq7mToT53FW/KIZu80BXS4NdQ+rjbGOi3jdMjISdPVQrSlvPh/rDs6x8iU+PZ5zbOG6E3eDb6t8y0nkkGtI/yy/S/P15PnQYmeHhWC1ahPEXHUiOT+fk2ruE+sVRu005SpWPZc/M8YBEl/Y/wf10PE2e8YCb2NS4yybd3vhIzrQracRSBxtKiNp0IR8RP43/8mYTsBs3bjBlyhSGDRuWx5HlD7tvBTLlwD0qmhuwoX8d9a8kjXwM27uoNsjovhWqfJHlKUEJQYw4N4LAhEDmus7lS9svXzueeOUqwWPHIunoYLNlM/rOzkQGJnB8lQ+piRm0GlyVuNCrHPhlC5ZlbWlWoTeJ92O5ZPaENAN3dCqnMlNjGqmSEQvsrOlnZSZaTQj5Tr5M7CdOnCAsLCxHX9PS0pK2bdu+d8ybTXq/Q6kAACAASURBVMCuX7/OuXPnWLduHW3atGH+/Pk5GlNBIcsyi0/7ssLNn8Z2JVnRuxZGetrqfdOAK7CrF2jqwIBj2ap88YrwYrTbaDKVmaxttZY6lnVeO/5i23bCf/4ZXVtbyq5cgXaZMjy5Hc75LQ/RM9Tmi9HV8Dy2CV/3S9Ss3YYqijoEhYRw2cQHC+urXC9Vh6NSJ2yLabPWsRJVDIu9IxJByFv5MrHnlTebgLVt25Zp06ahr69Py5Yt8fHxoUaNGnkUXd5Iz1Qy8U8fDtwJpkedsszp5Ii2ulvMeu+GQyPAtCL03gsm5bI85WTASaZcnkIpg1KsaLGCCsYVXh2TMzII//lnYnbsxLB5c8osWohUTJ8bh//i9vEALCsa07CzOafXzCLq+TM+bzaUEs+N8Srmz33jm5g7+rJKdxD+kh19Spsw264s+qLNrpCP5cvEntWVdW5p2LAhurqqmmxnZ2eePHlSpBJ7fGoGQ7d64O4fzQ+t7BnZXM3tAf7u+XJhPlT4DLpthWLv788jyzIb7m1gmecynC2cWdZsGSZ6/9z3V8TFETx2LEnu1zD7ZjDmY8eSkSFzds1dnnpHUaVhaWyqJvLn/AlooU3XZpNJf5rCmRL3SDe5RIKtISs0ZqCjqctah/J0tBD9goT8L18m9vyidevW7Ny5E2NjY06fPs13332X1yHlmpDYFAZuuoV/ZCJLujrxdW1r9b6hIgOOjoE728CpJ3zxG2i9f2PrDEUGs6/P5qDfQdpWaMsc1znoav6zOCo9IIDnw4aTHhRE6fnzKdH5K2Ijkjmx+i4xoUm4dq1ESow7hxbvwKZcdVzNvyT0WQSXTLwwqXiNk2btuC41op6RDiur2VJGT40bbQtCDhKJ/T1mzJhBs2bN0NHRYejQoUWmCdiDkHgGbb5FYlommwfWpZGdmnuop8bD3v7gfx6aTIKmk7KsfIlLi2PchXHcDLvJUKehDHca/tpfE0nXrxM0egySJFFu00b0XVwIfBDN6fX3QYLW39lz98xm/G9fp37tzpRLsscryY9HJd3RrBbJIu2xxEolmVTBklHlSonNpYUCRST2t/i7CVizZs149OhR3gaTy676RfHdVg8MdbXYO7QBVUqruedLfAhs7waRD+HLFeDcJ8tTnic8Z8S5ETxPeM68RvPoWOn1LtExu3YRNnceOuXLUXbVKrStrblzJpBr+/0wtTKg/pcmnN84h/iICL5oNAYpWOKUkRcKyws8Lu/AYWkwZXQ02OpoRy1Rmy4UQCKxC68c9g7hhz1eVCxpyOZBdShtrOaqj/D7qkZeqXHQaw/YtsjylPdVvsiZmYT//Asx27dj0OQzyixZgqxTjLObH/D4RjiVnM2xdojm8OJFFNc3o0utCYSERuFudgs9ex+2Fu+Nv2RPFwtDfqlcAUN1t0cQBDURiV0AYNPVp8w68oC65U1Z188FY301lzP+dQF29wUdAxh4Akpn/VD65NOTTLkyBUsDS1a0WEF54/Kvjqkeko4jyd0d04EDsRj/A0nxGRz/zZPIwATqdLAhKeo8p1YepqrtZzhqu+IZ788zKzfCHYqxQ3MyuhrarKlSji8t1LzoShDUTCT2Ik6WZRae8mXVBX8+r1qK33o6o6et5itV711waCSUtFOVMxq//8GsLMusv7ue3+78Ri2LWvyv2f9eq3xJDwjg+dBhpAcHU3reXEp8/TUhT2I4ufYemRlKmvW1wef0WkIePaSlyyD0oo04qX8DRcUrnCjVBk+pLg2NtFhezR4r8YBUKAREYi/CMhVKJu+/y16PIHrVs2HOl45oaqi5nPHKUjg3G8o3hu7bsixnzFBkMOvaLA75H6JdhXbMcZ2DjuY/yTfJ3Z2gseNUD0k3bqCYiws+bkFc3fsEI/NiNPhcm4t/zEJKk+hcewIhMdFctDhBYpUotuiOIlkyZmalUgwpaymadwmFhkjsRVRKuoIROzw5/yiCMS3tGN3CTr016opMODEBbm+E6l1VD0qz2MLu35Uvw5yGMcxp2KsYZVkmZscOwuf/jG7FClivXImGpRXn/3jIo2thlKtuhnkZf06u2EJFS2ecSjfnVqIvkZXOc6NCTc5JfbHXU7KmehWxglQodERif8O/m4DNmDGDixcvAhAWFkb//v2ZPHlyHkf46eKSMxi4+SZez2OZ28mRPvWzXtn5SdKTYd8geHwCXMdAixmg8f6Vm/+ufJnfaD5fVPqnT4yckUHY3HnE7t6NYbNmWC1aSHK6FicXexLxLAHnVqWICjjE1Z3XaFy1B3qpZpwo5kaSgy9bi/cjQrJkSBkjfqpUHj2xglQohERi/5c3m4DNmjXr1bEuXbrQr1+/vAotx0TEp9Jv403+ikxiZe9atHFUc8vdpCjY0V3VnbHdYqj7bZaneEV48f3571GiZF2rdbhYurw6lhkTQ/DoMSTfvInZt99iPmY0If7xnFp3h8wMJQ07l+DO8WWkRSXyZY3RBCRHc6PsXrztrTmqOR5LLQX7HG1xNSmuzlkLQp7Kl4n98eM5JCQ+zNHXLG5YBXv7ae8d82YTsL/dunULa2trypQpk6Mx5bbA6GT6bLhBVGIamwbWwdVWzQuPXvwF275W1apnszvj+ypf0p484fnwES/b7S7EqEMHfM4HcfVPP4zNi+FYK5pLfyyjbImqOFXqyVWFN1E1b7HH7GsCpIp0NddhvkNliosyRqGQy5eJPa+82QTsb8uWLXvt6r0g8g1LoO+GG6QrlGz/pp76+6gHe6pq1GUF9DsMNvXeO1yWZdb6rGW51/K3Vr4kuLkRMn4CGvr6lNu2Fa3K1Tiz8QFPboVTztEYTekKV3ecw9WuC5KiBCdNDuFbVYcDWqMx0IQNVWxob2Gq3jkLQj6RLxN7VlfWuSk2NpaIiAgqVaqU16F8NM/AGAZuuoWetgZ7vmuAfSk134Z4cka12bSBGfTZryprfI8MRQYzr83ksP9hOlTswKyGs15VvsiyTPTadUT+73/oVa2K9coVJGsU59DC20SHJFGjaXGeem4hOfgFHaqO5J7iGU8d9nHIqg2+UlWaG8Myx2qY66i5Ll8Q8pF8mdjzk0OHDtGuXbu8DuOjXXkSxZCttzEvrsu2wfXUvznGnW1w+HsoVRV674Pilu8dHpcWxxi3MdwOv83wmsMZWmPoq8oXZUoKoVOmEn/8OEYdOlB67hwCnyRydtNtAGo2T8Pz2Cqs9R2oVaE9bvoX8HVMZZ/uMLQ0tPjVrhQ9rCzFRhhCkSMSexZOnTrF+PHj8zqMj3LqfhijdtyhorkBfwyui0VxvaxP+liyDJcWg9tcqNhU1XI3i82mA+MDGX5uOCGJIfzS+BfaV2z/6lhGaChBI0aS+vAh5j+Mw3TQYDxOPuPm0aeYWelhbOrBrT/P41qhM/EaWpy23cMJm8bclWrSwDCD5dWdRDdGocgSif0t/m4CBrBjx468C+QTHPIKZtweb2pYG7N5QF31tghQKuD4eFWNeo3u0HF5li13PcI9GO02GgmJ9Z+vp1apWq+OJXveIej775FTUrBeuQLtuo04vuouz+5FU766NtGBuwl9nMjn9t9xS9eD+06R7NMfhELSYV5FEwbZ2IirdKFIE4m9ENp1M5DJB+5Sr4Ip6/vXwVBXjR9zRgrsGwy+x6DRWFWNehZJ9Yj/EWa4z6CMYRlWtlhJWaOyr47F/vknoTNnoW1VmrJbNhOvbcGB+bdIik3Dvk4ijy5vw9agJkY2TThtc4hTFWpzR6M9NYulsKpGdSroq/GvEkEoIERiL2Q2XnnK7KMPaFrZnNV9aqu370vyC9jZA57fhLYLod77NyKRZZkVXitY47OGupZ1Wdp0Kca6xqpjGRmqzow7dmDQsCFlfl2K770kLu30QM9AwtruLr5nr+Ba7mv89INxq3mZPw17kSHpMbWcIcMqOIme6YLwkkjshcgKNz8WnfKlTTVLlvWsia4667Vjn6tq1GOeQtfNUK3Te4enKdKYdmUaJwJO0NmuM1PrTUVbU3V7KPPFC9Wio1u3MB04ENPvx3Bxnz8Pr4ZiUU5BcvRh4r2gXsXeXCl7nhN2jtzR6E913SRWOlXDzkDND4QFoYARib0QkGWZRad8WXnBn6+cy7CoSw201LlUPvy+KqmnJ0PfA1C+0XuHR6dEM9ptNN6R3oytPZaB1Qa+ugeecv8+QaNGoYh+gdWihUgNWnLgV28iAxMo6xBJ4J0DVDNuREJ5LfbWvMR+oy6kSXpMttFjZEVxlS4IbyMSewEnyzJzjj5k49Wn9Kxrw7xOjmios0NjwBXY2UvVR33QCShV7b3D/WL8GHl+JNEp0fza9Fdalmv56ljc0WOETp2KpokJ5bZvJ0xZinPzb6FUpFOqrAcRtx9Sz6YrN6yvc8LeDg/NvlTViWe1U1XsDcXORoLwLqID0hvCw8Np3LgxAJ6enrRs2RJXV1eWLFmSx5H9l1IpM+PwfTZefcqAhuWZ/5Wak/r9g7D1K1Vt+uDTWSZ192B3+p7oS5oijc1tNr9K6rJCQfiiRYSMH4+eYzXK7d7Dnce6HF/pg55+HJrsRTsgBetKjdhd5wb/c+iIj6YzP1prcaZhY5HUBSEL4or9X95sAjZq1Ch27dqFtbU1rq6udO7cmQoVKuRxlCpKpcyUg/fYeTOQIZ9VZHJbB/WW+N1YCyd+hLL1oOdO0H//8vxdj3bxy81fqFSiEitarMDSQLVQKTMmhpAfxpPk7k6Jnj0oPnwcR7c8JuRJLBZln/HisRvVzVvi4/SIQw4SXpq9qKody6qaVahsaKi++QlCIZKtxC5J0gagKnBMluW5bzluDOwCNIEkoLssy+kfG9S0J0HcS0z52NPfytGwGHPs3r9Tz5tNwF68eEHZsqpSPDMzM+Lj43M0po+lUMpM3u/DnttBDG9aiQmtK6svqcsynJ8Dl5dA5fbQZQNov7t/eaYyk0W3FrHj0Q6aWDdhwWcLMNBWXWGnPnxI0MhRZEZEUHruHBIdm7NnoRfpKYmUMHNH4Z+Ibfnm/On8iIPG7cmQdJhkLTHKtom4ly4IHyDLxC5JUmdAU5blBpIkbZQkyU6W5SdvDOsNLJVl+YwkSauANsBhNcSrVm82AXN1dWX58uWYmpoSEBBAjRpZ78upbgqlzIS93uy/E8zoFnaMaanGDTIUGXBkNHhth9oDoN0S0Hz3j0xCegITLk3gavBV+lftz9jaY9HUUFXmxB05Sui0aWgaG2Oz9Q8ehJTg5jIvihlGopFxmtIJtfCrHc4mBwkfze5U03rBauca2Bm+f/WqIAj/lZ0r9qbAnpffnwYaAa8ldlmWV/7rP82BiDdfRJKkIcAQABsbm/e+YVZX1rllzZo1uLm5MX36dCZOnJjnqxkzFUrG7fHmsHcIP7SyZ1SL9zfX+iTpSapGXn5noOlkaDLxvQuPghKCGHV+FAFxAcxoMIMu9l0AkDMziVi8hBebN1PMpTZmcxdz9nAYgff9MDa9izLkMRVtGnC41jMOG7dBgTaTrGRG2TcTV+mC8JGyk9gNgOCX378Aar1roCRJDQATWZavv3lMluW1wFoAFxcX+cNDzX2amppUrlwZgN69e+dpLJkKJaN3e3HMJ5SJbRwY1lSN3SaTomBHNwi5Ax3+By4D3zvcK8KL0W6jyVBmsLrVauqVVrXozXzxguCx40i+cQOTPn3I7DyEfat8SYmPRr+YG2axljyra8m8yno81PwaJ61IVtWqT0UDsQmGIHyK7CT2RODvm6qGvKOSRpIkU+B34OucCS1/mDp1KgsWLMjTq/V/J/Up7arw7WcV1fdmMQGwtTPEB6saeVXp8N7hh/0PM9N9JqUNSr+2MUaKjw9Bo8egiI7Gcv7P+OvV5Obvd9HW9adY+m3KmDhzqGkER41aIyEz01pmiG1LsaG0IOSA7CR2D1S3X64DToDvmwMkSdIB9gKTZVl+lqMR5oF/NwHbsmVL3gWCKqmPya2kHuoD27tAZir0PQjlGrxzqFJW8pvnb2y4t+E/7QFi9uwhfM5ctCwssNiwjcvumQQ+eEixYu6YJWsSXLsMsyub4KdRHxetcFbWdsVGX1S8CEJOyU5iPwhcliTJCmgL9JAkaa4sy1P/NWYwqls0UyRJmgKskmV5d86HW7RkKpSM3ePNUZ9QfmrnoN6k/tdF2NVb1Wp30CmwqPLOockZyUy6PAm35250se/CT/V+QltDG2VaGmFz5hC3708MGjWCYdM4tCeQ5NhnGMjuWOg7cLB5IicNW6BDBvPKygyq9HmeP7sQhMImy8Quy3K8JElNgVbAQlmWwwDvN8asAlZ9ajCyLBeoX3JZVt+jgkyFkh/2enPEO4RJbR0Y8pka76nf2w8HvgPTitDnTzB+98Pr0MRQRp0fxZPYJ0yqO4leDr2QJImM4GCCvh9N6v37mA4bRkD59txa9xgtDQ9KKeMIcinFKltrAjUq4KodwgqXpljqiR4vgqAO2apjl2U5hn8qY9RCT0+P6OhozMzMCkRyl2WZ6Oho9PRyvk2sQinzw15vDnmFMLGNA0ObqDGp31gDJyaCTX3VwqNi794L9e+HpOmKdFa0WEGjMqoeMYlXrxLyw3hkhQKTxStw9y1B0FEv9DWuYmZszX5XU87qN6M4SSwrr0H3CgV3RypBKAjyzcpTa2trgoKCiIyMzOtQsk1PTw9r65wtzVQoZca/TOo/tqmsvuoXWYZzs+DKr9laeHTE/wgz3WdioW/BxtYbqVSiErJSSdTq1UT9vhxdW1sU3//MkRNRpCVcxUIKIrCOKcsrViZUKkNLnSCWubTATPfd7yEIQs7IN4ldW1s73yzXzytKpcykP304cCeYCa0rM7yprXre6AMWHimUCpbdWcame5uoY1mHJU2WYKJnomoNMHEiSZcuY/BFR54598d771/ocAXLUqbsbWjNJT1XTIllXSUtvrB5f3WNIAg5J98k9qJOlmWmHbrHXo8gxrS0Y0QzNSX1fy88ajIJmk5658KjxPREJl6eyKWgS3Sz78akepPQ1tAm5e5dgkaPRhEZhf6Ps7keWo6wc+6Ya/rxxLU4y8o68wIzOuoFs7hOa4pri71HBSE3icSeD8iyzOyjD9h+I5BhTSsxWl0rSpOiYHtXCPXKcuHR84TnjDo3ioD4AKbUm0IPhx7IskzMrl2Ez5uPhnlJ0qZt4MLlWEg+jpm1DjsbVOSmbl2s5HB2ORjSxOoL9cxDEIT3Eok9j8myzIKTvmy6GsDgRhX4UV0NvV48VW2OER8M3beBQ/t3Dr0ZepNxF8chyzKrW62mfun6KJOTCZs1i7hDh9Fp3JzHNQfjd/oBppr3uN+8BHtLNyAZA3oXe868Om3Re09PGUEQ1Ev89uWx/519wuqL/vSpb8PU9lXUk9RDvWFbF1CkQ79DqgqYd9j9aDe/3PwFGyMbfm/+OzZGNqT5+RE0Zgzp/n/BoAlcibEl8fZJDCop2Vy3Kne1a1BRGcRv1W1wsXDJ+fgFQfggIrHnoRVufiw794RuLtbM7uionqTu7wa7+4KeMfQ/AhYObx2Wocjg55s/s/fxXhqXacyCzxZQXKc4cYcPEzpjJugb8mL0au54hFFc6ySP25pwqKQrSjQYZhjElNrt0NIQ+7YIQn4gEnse2XjlKYtO+dKpphU/d66hnp2P7u6DA0OhpB303gfGZd46LDolmnEXxuEZ4ck31b9hZM2RSOkZhE6bTuzevVCnKfcc+hJ+wx3NKqmsc3bGT8sOR+VTVjjXo7Lpu/8CEAQh94nEngd23wpk9tEHtHW0ZHFXJzTVkdTdl8PpKVDOFXpsf+fCo4fRD/ne7XtiU2NZ+NlC2lZoS3pAAEFjxpL66BFJPX7EI8oEvZDjeHcsyQnj1uiSxk8lwhlVs1OBWEwmCEWNSOy57Ih3CJP236WJvTnLejijpZnDty+USjgzDa4thyodofM60H776tgTT08w/ep0SuiVYEvbLVQ1q0r8iROETp1Gpq4hT/uu4Jn/XVJrhrCuWj2CNcpSX/GY5fVaYl38/VvjCYKQd0Riz0VnH4QzdrcXdcqbsrpPbXS0cjipZ6bDwWFwbx/UHQJtfoGXOxj9m0Kp4Pc7v7Ph3gZqWdRiadOlmEgGhM6YSezu3STXbo23ZUuUERe58pUFFwzaUoJYFpaMpV/1bjkbsyAIOU4k9lzi7hfF8B2eVLMyYkN/F4rp/DfhfpLUeNjdB55ehJYzwXXMWxcexaXFMfHyRK4GX1V1Zqz7E8pnzwkYO5iUx36EdprK48hYoirfZbdtI6Ilcz5XPuR/DTtgWkxsgCEIBYFI7LnAMzCGb/64TQUzAzYPrEtxPe2cfYOEMFUf9YiH8NUacOrx1mFPYp4w2m00oUmhTG8wna72XYk7dIjQWbNJNirLgw7zSVTe4WQXa27quVJaGcbGsmm0s+uZs/EKgqBWIrGr2f2QOAZsvIlFcV22Dq6LiUEOL6+PfKxaeJQcDb12g23Ltw478+wMU65MwUDbgE2tN1HD0J6QyT8Re+AgYfX78FjbhKfVH/GndTNS0Ker/IAFn32NvrZuzsYrCILaicSuRk+jkui/8SYGulps+6YeFkY53OI38Drs7AEaWjDwGFg5/2eIQqlghdcK1t1dRw3zGvza9FeMnsfwdGA3EoKi8W0znUjjJ+xvaMwDnQZUUgSwyM6EhuV65WysgiDkGpHY1SQsLpU+62+glGHbN/WwNsnhTSUeHoE/vwGjMqrNMUz/2xkzLi2OSZcncSX4Cl/bfc3kupNJ2r2PgAULCS9bn0cN2+LTIIQj5q3QQGaIxiOmN+kmFhoJQgEnErsaxCSl03fDDeJSMtj5bX0qmefwfp4318HxCVCmNvTaAwZm/xni+8KXMW5jCEsOY1r9aXS2aEXomB+IuXAN3wZDeV7pBXtcrAjQrECNjEf85lQPh1Lv3uNUEISCQyT2HJaUlsnAzbd49iKZLQPrUt3aOOde/LXNMdrB1xtA579/CRz96yiz3GdhpGPEptabsH+WwdPvOhOmMOdBswG4N1dw1rg1BiQxWfsvvm/aXSw0EoRCRCT2HJSWqWDoNg/uBsexqnctGlT675X0R8tMh8OjwGcX1B4I7Rb/Z3OMDGUGS24vYfvD7dQuVZtFrr/A5n34r9nA4+pdedhQYk9VOyI0LGmU5sNvDdpgZWyRczEKgpAviMSeQxRKmXG7vbn8JIrFXZ34vJplzr14apyqkdfTi9BsKnw2/j816lEpUfxw4Qc8IzzpU6UPo0p3J+K7Hwjxi+Vu676calYcd4M6WCjDWVo8nF7N+uVcfIIg5CsisecAWZaZevAex+6GMrV9FbrUzsF9UOOCVZtjRPlCp9VQ87815V4RXoy7MI6E9AQWNF6A6wOZgBE98bVqys0hTvxZsRaJFKd9qidLm3bFWCw0EoRCTST2HLD0zGN23gxkRLNKfNO4Ys69cPh9VR/1tATovRcqNX/tsCzLbHu4jaW3l1LasDQrGyzFaPkuHp6/w+2WnTncpDQ+uo6Uy3zG8tJafO44KOdiEwQh3xKJ/RNtvRbA7+f96FGnLOM/r5xzL/zXRVWLAB0DGHQCLKu/djgpI4npV6dz+tlpmpVtxnSjHrwYNIkbxapxfmxrjlg2QIlE71RP5rfqg66W2HdUEIoKkdg/wfG7oUw/fJ+WVUoxt1MObpThswcODgczW+izD4xfv7XjH+vPGLcxBCYEMrbmaL64moH/5plc/aI5++rb85dWRapm+LLItiq1K4qrdEEoakRi/0jX/KMZs8uLWjYm/N4zh9rvyjJcXgzn50L5xqq9SYuVeG3I8b+OM/PaTPS19NngOB/TX3ZwMd2cYxM7ctqkHsVI5ft0Hya16oOGWGgkCEWSSOwf4UFIPEP+uE05M/2c69SoyIBj48DzD6jeDb5cDlr/9GlJV6Sz+PZidj7aSS1zZ+bEtyB81Ep2dm7M3ppOhGmUpn6KF7+6NKeCReNPj0cQhAJLJPYP9PxFMv033cRQT4stg+pSQj8H7l2nxsPeAeB/Dj6bAM2mvFbOGJQQxPiL47kffZ/BZbvRaX8El+N8ODCpE1cM61BSGclsHjOk3YBPj0UQhAJPJPYPEJ2YRr+NN0nLULB9WEOsShT79BeNC4Yd3VQtdzv+DrVery93C3RjytUpIMOq4t+hPf88a7vWZ79dHeIwonXSLZY07kxJ4xxcDCUIQoEmEns2paQrGLzlNiGxKWz/ph72pXKgFjzsnqpG/e9yRtsWrw5lKDP4zfM3Nt/fTA3Dysy4Y8uV6GfsHt8Zb11HbBSBLDBM48vm3356HIIgFCoisWeDQikzaucdvINiWdW7Ni7lc2C/T7+zsGcA6BaHQSfB0vHVobCkMCZcnIBXpBdDtVpQa3Mky7tbcNiqPko06RZ/nQVtB1BMJ4fbAAuCUCiIxJ4FWZaZcfgeZx+GM6tjNdo45kCrgNsb4dh4sKgKvfeAkdWrQ5eCLjHlyhQU6Wmsftocr1RDxn/fGH+tSlRJ92WuVTlcmw/99BgEQSi0spXYJUnaAFQFjsmyPPcdY0oB+2RZLlQlGasv/sW264F891lF+jcs/2kvplTCmWlwbTnYtYYuG1RX7Lx+68U1vRxd3SxZ39mO06b10SOFofE3mdZhMJqaObxXqiAIhU6WiV2SpM6ApizLDSRJ2ihJkp0sy0/eGGMCbAEM1BRnnjh4J5gFJx/R0cmKiW0cPu3F0pNh/7fw6CjU/Q5az3/VnTE4MZgfL/7I3UhvJj915rmeLeMH1yFUw4q6KXdYVNWVyuUL1b+XgiCoUXau2JsCe15+fxpoBDx5Y4wC6A4cyrHI8pi7XxQT9nlTv6Ipi7rWQEPjE1aVJoSptrAL9YY2C6D+P7dSzj47y/Sr0ykZk8ksnybsaO/E5eJ1MVNGMiXJh1EdBubAbARBKEqyk9gNgOCX378Aar05QJbleOC9/CU9YQAADLJJREFUS+olSRoCDAGwsbH50Dhz1aOweL7b6kGFkgas6euCrtYn3P4Ivw/bu0FKDPTYCZXbAJCmSGPJ7SXsfLiDvo9sSLBpzOTu9YnDiBYJN1ja8EtKlWyVQzMSBKEoyU5iTwT+Ltg2BD5qnbosy2uBtQAuLi7yx7xGbgiLS2Xgplvo62qyeWBdjItpf/yLPT4N+waBrqGqkVdpJwD+ivuLHy/+SOSzR4x72oLdrVzw0qtOWUUgM6VYenT8LodmIwhCUZSdxO6B6vbLdcAJ8FVrRHkoMS2TQZtvEZ+Swd6hn7AASZbh+io4PQVKOULPXWBcBlmWOeB3gF9u/Ewzn2KUcRzA7A4NyUSLr2PcWdh2AAbFcnjTa0EQipzsJPaDwGVJkqyAtkAPSZLmyrI8Vb2h5a5MhZJROzzxDU9gfX8XqloZfdwLKTJUG017bIIqX8BXa0DHgPj0eGa5z+Lm/VP0DmvDnlYN8NeqhEO6LzNLlKJp8+E5OyFBEIqsLBO7LMvxkiQ1BVoBC2VZDgO83zG2aY5Gl0tkWWbWkQe4+UYyt5MjzSp/5D6gKTGwp79qC7tG46D5NNDQwCvCi4kXf6TarQzs6nzHwioN0COFwdHuzOo0BC0tsZxAEISck62MIstyDP9UxhQ6G648Zev1Zwz5rCJ96pf7uBeJ9lf1fIl59moLO4VSwTrv1ey8sorWSV+wt3XDVyWM8yrWprq4ShcEQQ2K/KXiyXthzDv+kLaOlkz62Fr1vy7Cnn6goQn9j0C5BgQnBjP50iQsLsdg0WAEv70sYZz4woOxXw/O2UkIgiD8S5FO7F7PYxmz+w5O1iX4tXvND69Vl2W4tR5OTISS9tBzJ5hW4OhfR1l+ai616MD+Vq7EYUTL+OssrNcRK0tRwigIgnoV2cT+/EUy32y5hXlxXdb3d0FP+wNr1TPT4cQE8NgM9m2h81riNWDuxQlonQuFBiPYqFedsornTE2NoM+Xor+LIAi5o0gm9oTUDL7Zcpu0TCW7htSnpKFu1if9W1KU6tbLs6uvHpJ6RN5hwYGJlNZvzd6mX5GJFp2jr/BL634YFf/IChtBEISPUOQSe6ZCyaidd/CLTGTLwLrYWnxgX/Wwe7CrJyRGQOf1ZFTrxArPZUSfekJInaFc0rbFId2Xn/RM+bzLSPVMQhAE4T2KXGKfe+whF3wjmf9VdRrZlfywkx8egf3fgZ4RDDzOE30jlm7oTZpJI043GIguqQwMv8zsr4eirf0JK1YFQRA+QZFK7FuvBbDZPYDBjSrQq94H9KtRKuHCfLi0CMrURtltK1sDz+C35xHXawwgVMOKOilezCpTg1rNR6ktfkEQhOwoMon90uNIZh55QAsHC35qVyX7J6bGwf4h8PgkOPchtMkEfts5Gz+r2lyu2QMzZRQ/hF1jQs9h6gteEAThAxSJxP4kPIER2z2xszBkWU9nNLNb1hjpC7t6QUwActtFHDYqifvuPzhk3504jGkef51fnNtg06KleicgCILwAQp9Yo9OTGPQllvoamuyYUAdDHWzOeVHx1T307X1iOq5nVWnz3C1YjG87DtirXjOxJggBnYVJYyCIOQ/hTqxp2cqGbbNk4j4NHYNqU+Z7HRrVCrh4i9wcQFY1eK40wBOXr/LkSpfk4kWnaIus+DzfhgbG6t/AoIgCB+h0CZ2WZaZdvAeNwNe8FtPZ5xtTLI+KfmFavs6v7PEOXVjRag5x+IN8bd2wiHDlwlKPdp3FQ9HBUHI3wptYt90NYDdt58zqrktHZ2ssj4hxAv29IWEME5WH85uRWlOOzREjxQGhF5gdpfh6OjoqD9wQRCET1QoE/vFx5HMPfaA1tVKMbalfdYneP4Bx8aTYGjOr6bDOVCi3ssSxjvMMK2MS68x6g9aEAQhhxS6xO4fmcjIHZ7YlyrO0m5ZNPbKSIXj4+HOVg6ZtGZbhZYvN5KOYmzQZSb2FbddBEEoeApVYo9LVvWA0dHUYH1/FwzeVwETEwB7+hMf6s0vVhPYb9uQOIxpEXeduY7NqSBKGAVBKKAKTWLPVCgZscOToJhkdn5bH2uT9+wd+vAIHBzBTtmFLfV+f7mR9HPGR/jzTS9RwigIQsFWaBL73GMPueIXxcIuNXApb/r2QZnpcGY6Ee7rmGc/kcNlGqlKGCMvMb9lL0xNP7B3jCAIQj5UKBL7nlvPX/WA6eZS9u2DYp7B3gGsiSnP1sZr8NO2xSHDlzEpEp26fZ+7AQuCIKhRgU/sHs9imHrwHo3tSjK57Tu2tnt0DL89k5hf5VtO2zZAlzT6BZ9nTtcR6Op+YC92QRCEfK5AJ/awuFSGbvPA0liP33s6o6Wp8fqAzDTk09NZ8jiT7a4LVCWMyXeYYlSB+n3G5U3QgiAIalZgE3tqhoLvtnmQlJbJtsH1KKH/xuKhSF9u/DGBxXbtuexUDzNlFKMC3JgycGzeBCwIgpBLCmRil2WZKQfu4f08ltV9alPZsvi/DyJ7bGa6xzP2Oo9RdWGMu85s+8+wFSWMgiAUAQUysW+6GsCfnkGMbmFHG0fLfw4kv+DY+qn8btcAL/tOlFU8Z3TIQ4b1G5F3wQqCIOSyApfYr/pFMe/4Qz6vWorRLexe/f+kB2f5ycOTw459yESLLyMuMq95T0q2/CIPoxUEQch9BSqxB0YnM2KHJ5XMDVja/WW7gMw0Nq+ZzXo7Z/ysP8ch3ZfhCel06z46r8MVBEHIEwUqsStlmUrmhizp6oShrhbBd84yze8Bp6t0QpdU+jw/y9xuI9HT08vrUAVBEPKMJMtyrr+pi4uLfPv27Y86V5ZlJFnJr2vm8od9nVcljOP1rWjSrHUORyoIgpB/SJLkIcuyS1bjCtQVO4D3pWPMiwvmssOXmCmjGPH0DNMGTcjrsARBEPINjayH5B8r1i2gh0KfK4YuNI+7xp+lSoqkLgiC8IYCdcXu4lCb0skRjAz2ZuQgsdBIEAThbQpUYq/XuCVueR2EIAhCPpetWzGSJG2QJOmaJElTP2WMIAiCoH5ZJnZJkjoDmrIsNwAqSpJk9zFjBEEQhNyRnSv2psCel9+fBhp9zBhJkoZIknRbkqTbkZGRHx6pIAiCkC3ZSewGQPDL718ApT5mjCzLa2VZdpFl2cXc3PxjYhUEQRCyITuJPREo9vJ7w3eck50xgiAIQi7ITgL24J9bK05AwEeOEQRBEHJBdsodDwKXJUmyAtoCPSRJmivL8tT3jKmf86EKgiAI2ZHlFbssy/GoHo5eB5rJsuz9RlJ/25i4nA9VEARByI48aQImSVIk8CyLYSWBqFwIJ78qyvMXcy+6ivL8szP3crIsZ1l9kieJPTskSbqdnS5mhVVRnr+Ye9GcOxTt+efk3EX1iiAIQiEjErsgCEIhk58T+9q8DiCPFeX5i7kXXUV5/jk293x7j10QBEH4OPn5il0QBEH4CCKxC0I+JUmSqSRJrSRJKpnXsQgFS54n9qLe6z2b8y8lSdLl3IwrN2Q1d0mSjCVJOiFJ0mlJkg5IkqST2zGqSzbmbgIcBeoCbpIkFarOedn9nX75s38nt+LKDdn47LUkSQqUJOnCy6/qH/oeeZrYi3qv92zO3wTYgqqDZqGRzc+1N7BUluXPgTCgTW7GqC7ZnHsNYJwsy/OAU0Ct3IxRnT7wd3ox/zQYLPA+4LPfKcty05dfdz/0ffL6ir0pOdDrvQBrStZzUwDdgfhciim3NCWLucuyvFKW5TMv/9MciMid0NSuKVnP/aIsy9clSfoM1VX7tdwLT+2ako3faUmSmgNJqP5RLyyakvXc6wMdJEm6+fLq/oO3MM3rxJ4jvd4LsOz0sY8vpL13sv25SpLUADCRZfl6bgSWC7I1d0mSJFT/qMcAGbkTWq7Icv4vb7tNAyblYly5ITuf/S2gpSzLdQFtoN2HvkleJ/ai3uu9MM8tK9mauyRJpsDvwKBciis3ZGvussoIwAfomEux5YbszH8SsFKW5dhciyp3ZGfuPrIsh778/jbwwbef8zqRFPVe74V5blnJcu4vr9r2ApNlWc6qaVxBkp25T5Qkqd/L/ywBFKYEl52f+5bACEmSLgA1JUlanzuhqV125r5VkiQnSZI0gU6A9we/iyzLefYFGL0Meinw8OVE52YxxjgvY87t+f9r7IW8jjcPPvthqG5DXHj51T2v487FuZsAZ4BLwEpeLiYsDF8f8nP/cvyFvI45lz97R1R/pd0F5n3M++T5ytOXVR+tgEuyLL/1IUl2xhRUhXluWRFzL5pzh6I9/9yYe54ndkEQBCFn5fU9dkEQBCGHicQuCIJQyIjELgiCUMiIxC4IglDIiMQuCIJQyPwf8JAWDQEa6aUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.special import comb\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "#(b)\n",
    "#计算Qk\n",
    "def Q(k, x):\n",
    "    s = 0\n",
    "    for i in range(0, (k+1)//2):\n",
    "        s1 = x ** (i + 1) * (1 - x) ** (k - i)\n",
    "        s2 = (1 - x) ** (i + 1) * x ** (k - i)\n",
    "        s += comb(k, i) * (s1 + s2)\n",
    "    return s\n",
    "\n",
    "x = np.arange(0.01, 0.5, 0.01)\n",
    "K = np.arange(1, 20, 2)\n",
    "for k in K:\n",
    "    result = []\n",
    "    for i in x:\n",
    "        result.append(Q(k, i))\n",
    "    plt.plot(x, result, label = str(k))\n",
    "    plt.legend()\n",
    "plt.title(\"$Q_k$ VS $\\eta$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 6.1 (Page 42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#(a)\n",
    "import numpy as np\n",
    "import helper as hlp\n",
    "\n",
    "X = np.array([[1, 0], [0, 1], [0, -1], [-1, 0], [0, 2], [0, -2], [-2, 0]])\n",
    "y = np.array([-1, -1, -1, -1, 1, 1, 1])\n",
    "\n",
    "knn = hlp.KNeighborsClassifier_(1)\n",
    "knn.fit(X, y)\n",
    "hlp.draw(X, y, knn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "knn = hlp.KNeighborsClassifier_(3)\n",
    "knn.fit(X, y)\n",
    "hlp.draw(X, y, knn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#(b)\n",
    "#特征转换\n",
    "Z = np.c_[np.sqrt(X[:, 0] ** 2 + X[:, 1] ** 2), np.arctan(X[:, 1] / (X[:, 0]  + 10**(-8)))]\n",
    "knn = hlp.KNeighborsClassifier_(1)\n",
    "knn.fit(Z, y)\n",
    "hlp.draw(X, y, knn, flag=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "knn = hlp.KNeighborsClassifier_(3)\n",
    "knn.fit(Z, y)\n",
    "hlp.draw(X, y, knn, flag=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 6.2 (Page 42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import helper as hlp\n",
    "    \n",
    "X = np.array([[1, 0], [0, 1], [0, -1], [-1, 0], [0, 2], [0, -2], [-2, 0]])\n",
    "y = np.array([-1, -1, -1, -1, 1, 1, 1])\n",
    "\n",
    "#(a)\n",
    "X1 = np.array([[np.mean(X[y>0][:, 0]), np.mean(X[y>0][:, 1])], [np.mean(X[y<0][:, 0]), np.mean(X[y<0][:, 1])]])\n",
    "y1 = np.array([1, -1])\n",
    "\n",
    "knn = hlp.KNeighborsClassifier_(1)\n",
    "knn.fit(X1, y1)\n",
    "hlp.draw(X, y, knn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#(b)\n",
    "def f(X):\n",
    "    while(len(X) >1):\n",
    "        #记录当前距离\n",
    "        d = float('inf')\n",
    "        #元素数量\n",
    "        n = len(X)\n",
    "        #记录最优元素的下标\n",
    "        k = 0\n",
    "        l = 0\n",
    "        for i in range(n):\n",
    "            for j in range(i+1, n):\n",
    "                d1 = np.sum((X[i] - X[j])**2)\n",
    "                if(d > d1):\n",
    "                    d = d1\n",
    "                    k = i\n",
    "                    l = j\n",
    "        #生成新的元素\n",
    "        data = (X[k] + X[l]) / 2\n",
    "        #删除元素\n",
    "        X = np.delete(X, l, axis=0)\n",
    "        X = np.delete(X, k, axis=0)\n",
    "        #增加新元素\n",
    "        X = np.append(X, data.reshape(-1, 2), axis=0)\n",
    "    return X[0]\n",
    "\n",
    "#划分数据\n",
    "X_pos = X[y>0]\n",
    "X_neg = X[y<0]\n",
    "\n",
    "#新数据\n",
    "X2 = np.array([f(X_pos), f(X_neg)])\n",
    "y2 = np.array([1, -1])\n",
    "\n",
    "knn = hlp.KNeighborsClassifier_(1)\n",
    "knn.fit(X2, y2)\n",
    "hlp.draw(X, y, knn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 6.4 (Page 42) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import helper as hlp\n",
    "\n",
    "#Step1 产生数据\n",
    "#参数\n",
    "rad = 10\n",
    "thk = 5\n",
    "sep = 5\n",
    "\n",
    "#产生数据\n",
    "X, y = hlp.generatedata(rad, thk, sep, 100)\n",
    "\n",
    "knn = hlp.KNeighborsClassifier_(1)\n",
    "knn.fit(X, y)\n",
    "hlp.draw(X, y, knn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "knn = hlp.KNeighborsClassifier_(3)\n",
    "knn.fit(X, y)\n",
    "hlp.draw(X, y, knn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 6.13 (Page 45)\n",
    "\n",
    "(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import helper as hlp\n",
    "\n",
    "\n",
    "#### (a)\n",
    "def Data(n, flag=1, scale=0.15):\n",
    "    \"\"\"\n",
    "    生成n个点，flag=1表示圆心固定\n",
    "    \"\"\"\n",
    "    if flag:\n",
    "        #中心\n",
    "        center = np.array([[0, 1, 0, -1], [1, 0, -1, 0]]).T\n",
    "    else:\n",
    "        #按极坐标方式生成点\n",
    "        theta = np.random.uniform(0, 2 * np.pi, size=4)\n",
    "        center = np.c_[np.cos(theta), np.sin(theta)]\n",
    "    #生成X\n",
    "    X = np.random.normal(scale=scale, size=(n, 2))\n",
    "    #生成每个数据对应的分类\n",
    "    index = np.random.randint(0, 4, size=n)\n",
    "    #增加中心\n",
    "    X += center[index] \n",
    "    #生成标签\n",
    "    y = np.copy(index)\n",
    "    y[y%2==1] = -1\n",
    "    y[y%2==0] = 1\n",
    "    \n",
    "    return X, y\n",
    "\n",
    "# =============================================================================\n",
    "# CNN1\n",
    "# =============================================================================\n",
    "def CNN1(X, y, k=1):\n",
    "    n = X.shape[0]\n",
    "    #初始化\n",
    "    index = np.random.choice(np.arange(n), size=k, replace=False)\n",
    "    #condense data\n",
    "    X_cd = X[index, :]\n",
    "    y_cd = y[index]\n",
    "    #剩余的点\n",
    "    X1 = np.delete(X, index, axis=0)\n",
    "    y1 = np.delete(y, index, axis=0)\n",
    "    \n",
    "    Ein = []\n",
    "    while True:\n",
    "        #训练knn\n",
    "        nn = hlp.KNeighborsClassifier_(1)\n",
    "        nn.fit(X_cd, y_cd)\n",
    "        #预测结果\n",
    "        y_pred = nn.predict(X)\n",
    "        #错误率\n",
    "        ein = np.mean(y_pred != y)\n",
    "        Ein.append(ein)\n",
    "        \n",
    "        if ein != 0:\n",
    "            #找到分类错误的点\n",
    "            i1 = np.where(y_pred != y)[0][0]\n",
    "            #找到y1中和y[ii]相同的点的索引\n",
    "            i2 = np.where(y1 == y[i1])[0][0]\n",
    "            #添加至condese data\n",
    "            X_cd = np.r_[X_cd, X1[i2, :].reshape(1, 2)]\n",
    "            y_cd = np.r_[y_cd, y1[i2]]\n",
    "            #删除该数据\n",
    "            X1 = np.delete(X1, i2, axis=0)\n",
    "            y1 = np.delete(y1, i2, axis=0)\n",
    "        else:\n",
    "            break\n",
    "        \n",
    "    return X_cd, y_cd\n",
    "\n",
    "# =============================================================================\n",
    "# CNN2\n",
    "# =============================================================================\n",
    "def dist(X1, X2):\n",
    "    \"\"\"\n",
    "    计算X1, X2每一项之间的距离\n",
    "    \"\"\"\n",
    "    d1 = np.sum(X1 ** 2, axis=1).reshape(-1, 1)\n",
    "    d2 = np.sum(X2 ** 2, axis=1).reshape(1, -1)\n",
    "    dist = d1 + d2 - 2 * X1.dot(X2.T)\n",
    "    \n",
    "    return dist\n",
    "\n",
    "def influence_set(d1, d2):\n",
    "    \"\"\"\n",
    "    根据距离生成全体influence_set, 用字典存储\n",
    "    d1为标签相同的点的距离, d2为标签不同的点的距离\n",
    "    \"\"\"\n",
    "    #计算不同标签的最短距离\n",
    "    d3 = np.min(d2, axis=1)\n",
    "    #找到相同标签中小于最短距离的部分\n",
    "    i1 = d1 < d3\n",
    "    #找到influence set对应的索引\n",
    "    u, v = np.where(i1)\n",
    "    #生成influence set\n",
    "    influe_set = {}\n",
    "    for i in np.unique(u):\n",
    "        #使用集合\n",
    "        influe_set[i] = set(v[u==i])\n",
    "        \n",
    "    return influe_set\n",
    "\n",
    "def influe_set_helper(i, key, X, influe_set):\n",
    "    \"\"\"\n",
    "    删除元素最多的influence set并返回对应的x\n",
    "    key为influence set所在字典的键，i为元素最多的influence set的索引，\n",
    "    X为点集，influe_set为influence set所在字典\n",
    "    \"\"\"\n",
    "    \n",
    "    index = key[i]\n",
    "    #需要删除的集合\n",
    "    x_del = influe_set[index]\n",
    "    x_del.add(index)\n",
    "    #influence set所在的字典\n",
    "    for j in key:\n",
    "        #如果索引不是influence set对应的x，则更新其influence set\n",
    "        if j != index:\n",
    "            #删除公共元素\n",
    "            influe_set[j] -= x_del\n",
    "            #如果为空，则删除该influence set\n",
    "            if influe_set[j] == set():\n",
    "                influe_set.pop(j)\n",
    "        #如果索引是influence set对应的x，则删除influence set\n",
    "        else:\n",
    "            influe_set.pop(j)\n",
    "    \n",
    "    return influe_set, X[index]\n",
    "\n",
    "def CNN2(X, y):\n",
    "    #将数据分为两类\n",
    "    X_pos = X[y==1]\n",
    "    X_neg = X[y==-1]\n",
    "    \n",
    "    #计算距离矩阵\n",
    "    dist_pos = dist(X_pos, X_pos)\n",
    "    \n",
    "    #设置对角线的值\n",
    "    np.fill_diagonal(dist_pos, np.inf)\n",
    "    dist_neg = dist(X_neg, X_neg)\n",
    "    \n",
    "    #设置对角线的值\n",
    "    np.fill_diagonal(dist_neg, np.inf)\n",
    "    dist_pos2neg = dist(X_pos, X_neg)\n",
    "    \n",
    "    #influcence set\n",
    "    influe_set_pos = influence_set(dist_pos, dist_pos2neg) \n",
    "    influe_set_neg = influence_set(dist_neg, dist_pos2neg.T)\n",
    "\n",
    "    #condense data\n",
    "    X_cd = []\n",
    "    y_cd = []\n",
    "    while True:\n",
    "        #计算influence set非空的数量\n",
    "        len_pos = np.array([len(influe_set_pos[i]) for i in influe_set_pos])\n",
    "        len_neg = np.array([len(influe_set_neg[i]) for i in influe_set_neg])\n",
    "        #得到键\n",
    "        pos_key = [i for i in influe_set_pos]\n",
    "        neg_key = [i for i in influe_set_neg]\n",
    "\n",
    "        \n",
    "        if (len(len_pos) > 0 and len(len_neg) > 0):\n",
    "            #找到最多元素的influence set\n",
    "            i1 = np.argmax(len_pos)\n",
    "            i2 = np.argmax(len_neg)\n",
    "            if len_pos[i1] > len_neg[i2]:\n",
    "                influe_set_pos, x = influe_set_helper(i1, pos_key, X_pos, influe_set_pos)\n",
    "                X_cd.append(x)\n",
    "                y_cd.append(1)\n",
    "            else:\n",
    "                influe_set_neg, x = influe_set_helper(i2, neg_key, X_neg, influe_set_neg)\n",
    "                X_cd.append(x)\n",
    "                y_cd.append(-1)\n",
    "        elif len(len_pos) > 0:\n",
    "            i1 = np.argmax(len_pos)\n",
    "            influe_set_pos, x = influe_set_helper(i1, pos_key, X_pos, influe_set_pos)\n",
    "            X_cd.append(x)\n",
    "            y_cd.append(1)\n",
    "        elif len(len_neg) > 0:\n",
    "            i2 = np.argmax(len_neg)\n",
    "            influe_set_neg, x = influe_set_helper(i2, neg_key, X_neg, influe_set_neg)\n",
    "            X_cd.append(x)\n",
    "            y_cd.append(-1)\n",
    "        else:\n",
    "            break\n",
    "        \n",
    "    return np.array(X_cd), np.array(y_cd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b)首先查看原始数据的分类结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 1000\n",
    "X, y = Data(n, 1, scale=0.5) \n",
    "plt.scatter(X[:, 0], X[:, 1], edgecolor='k', c=y)\n",
    "plt.show()\n",
    "#原始数据的分类结果\n",
    "nn = hlp.KNeighborsClassifier_(1)\n",
    "nn.fit(X, y)\n",
    "hlp.draw(X, y, nn, n=500, flag=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CNN1的算法结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### CNN1\n",
    "#condense data的分类结果\n",
    "X_cd, y_cd = CNN1(X, y)\n",
    "nn = hlp.KNeighborsClassifier_(1)\n",
    "nn.fit(X_cd, y_cd)\n",
    "hlp.draw(X_cd, y_cd, nn, n=500, flag=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CNN2的算法结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### CNN2\n",
    "#condense data的分类结果\n",
    "X_cd, y_cd = CNN2(X, y)\n",
    "nn = hlp.KNeighborsClassifier_(1)\n",
    "nn.fit(X_cd, y_cd)\n",
    "hlp.draw(X_cd, y_cd, nn, n=500, flag=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(c)如果取$\\sigma  =0.5$，那么这部分运行时间非常长，不建议运行，不过从之前的例子可以看出，算法2的产生condensed sets集合的元素数量要明显\n",
    "小于算法1。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "#### 运行时间较长，不建议运行\n",
    "m = 10\n",
    "NUM1 = []\n",
    "NUM2 = []\n",
    "for i in range(m):\n",
    "    X, y = Data(n, 1, scale=0.5)\n",
    "    X_cd1, y_cd1 = CNN1(X, y)\n",
    "    NUM1.append(len(y_cd1))\n",
    "    \n",
    "    X_cd2, y_cd2 = CNN2(X, y)\n",
    "    NUM2.append(len(y_cd2))\n",
    "    \n",
    "plt.hist(NUM1)\n",
    "plt.title(\"CNN1\")\n",
    "plt.show()\n",
    "print(\"Average sizes of the condensed sets is {}(CNN1)\".format(np.mean(NUM1)))\n",
    "\n",
    "plt.hist(NUM2)\n",
    "plt.title(\"CNN2\")\n",
    "plt.show() \n",
    "print(\"Average sizes of the condensed sets is {}(CNN2)\".format(np.mean(NUM2)))\n",
    "'''"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 6.14 (Page 45)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(a)划分数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import helper as hlp\n",
    "import numpy as np\n",
    "\n",
    "#### (a)\n",
    "#获得数据\n",
    "Train = np.genfromtxt(\"features.train\")\n",
    "Test = np.genfromtxt(\"features.test\")\n",
    "\n",
    "N = 500\n",
    "m = 100\n",
    "y_train, X_train = Train[: N, 0], Train[: N, 1:]\n",
    "y_train[y_train != 1] = -1\n",
    "y_test, X_test = Test[: m, 0], Test[: m, 1:]\n",
    "y_test[y_test != 1] = -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b)使用3-NN算法："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ein of 3-NN is 0.008\n",
      "Etest of 3-NN is 0.03\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### (b)\n",
    "#训练模型\n",
    "nn = hlp.KNeighborsClassifier_(3)\n",
    "nn.fit(X_train, y_train)\n",
    "y_test_pred = nn.predict(X_test)\n",
    "y_train_pred = nn.predict(X_train)\n",
    "\n",
    "#计算错误率\n",
    "ein = np.mean(y_train != y_train_pred)\n",
    "etest = np.mean(y_test != y_test_pred)\n",
    "print(\"Ein of 3-NN is {}\".format(ein))\n",
    "print(\"Etest of 3-NN is {}\".format(etest))\n",
    "#作图\n",
    "hlp.draw(X_train, y_train, nn, n=500, flag=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(c)使用C-NN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ein of C-NN is 0.008\n",
      "Etest of C-NN is 0.03\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### (c)\n",
    "X_cd, y_cd = hlp.CNN(X_train, y_train, k=3)\n",
    "#训练模型\n",
    "nn = hlp.KNeighborsClassifier_(3)\n",
    "nn.fit(X_cd, y_cd)\n",
    "y_test_pred = nn.predict(X_test)\n",
    "y_train_pred = nn.predict(X_train)\n",
    "\n",
    "#计算错误率\n",
    "ein = np.mean(y_train != y_train_pred)\n",
    "etest = np.mean(y_test != y_test_pred)\n",
    "print(\"Ein of C-NN is {}\".format(ein))\n",
    "print(\"Etest of C-NN is {}\".format(etest))\n",
    "#作图\n",
    "hlp.draw(X_cd, y_cd, nn, n=500, flag=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(d)重复多次试验，查看评价结果："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "meanEin of C-NN is 0.05360000000000001\n",
      "meanEtest of C-NN is 0.05788100000000001\n",
      "meanEin of K-NN is 0.01168\n",
      "meanEtest of K-NN is 0.024625000000000005\n"
     ]
    }
   ],
   "source": [
    "#%%time\n",
    "#### (d)\n",
    "N = 1000\n",
    "#索引\n",
    "train_index = np.arange(Train.shape[0])\n",
    "test_index = np.arange(Test.shape[0])\n",
    "\n",
    "Ein_KNN = []\n",
    "Etest_KNN = []\n",
    "Ein_CNN = []\n",
    "Etest_CNN = []\n",
    "\n",
    "for i in range(N):\n",
    "    #训练数据\n",
    "    train = Train[np.random.choice(train_index, size=m, replace=False)]\n",
    "    y_train, X_train = train[:, 0], train[:, 1:]\n",
    "    y_train[y_train != 1] = -1\n",
    "    #测试数据\n",
    "    test = Test[np.random.choice(test_index, size=n, replace=False)]\n",
    "    y_test, X_test = test[:, 0], test[:, 1:]\n",
    "    y_test[y_test != 1] = -1\n",
    "    \n",
    "    #训练KNN\n",
    "    nn = hlp.KNeighborsClassifier_(3)\n",
    "    nn.fit(X_train, y_train)\n",
    "    y_test_pred = nn.predict(X_test)\n",
    "    y_train_pred = nn.predict(X_train)\n",
    "\n",
    "    #计算错误率\n",
    "    ein = np.mean(y_train != y_train_pred)\n",
    "    etest = np.mean(y_test != y_test_pred)\n",
    "    Ein_KNN.append(ein)\n",
    "    Etest_KNN.append(etest)\n",
    "    \n",
    "    #训练CNN\n",
    "    X_cd, y_cd = hlp.CNN(X_train, y_train, k=3)\n",
    "    #训练模型\n",
    "    nn = hlp.KNeighborsClassifier_(3)\n",
    "    nn.fit(X_cd, y_cd)\n",
    "    y_test_pred = nn.predict(X_test)\n",
    "    y_train_pred = nn.predict(X_train)\n",
    "\n",
    "    #计算错误率\n",
    "    ein = np.mean(y_train != y_train_pred)\n",
    "    etest = np.mean(y_test != y_test_pred)\n",
    "    Ein_CNN.append(ein)\n",
    "    Etest_CNN.append(etest)\n",
    "    \n",
    "print(\"meanEin of C-NN is {}\".format(np.mean(Ein_CNN)))\n",
    "print(\"meanEtest of C-NN is {}\".format(np.mean(Etest_CNN)))\n",
    "\n",
    "print(\"meanEin of K-NN is {}\".format(np.mean(Ein_KNN)))\n",
    "print(\"meanEtest of K-NN is {}\".format(np.mean(Etest_KNN)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 6.24 (Page 49)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEXCAYAAAC3c9OwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAIABJREFUeJzt3Xl4leWd//H3N3vIDoQQZDNsIqsltaKowGini9VqbW1nqt1tFdvp/Dq97Dqt1trROk4dFZVWZ6xtbVXU0dZaW5VFitpgWURRdtmJQDYggSTf3x/nJIRwQhI4eZ6TnM/runLlLHdyPgHJx/u5z3M/5u6IiIi0lxJ2ABERSUwqCBERiUkFISIiMakgREQkJhWEiIjEpIIQEZGYVBAiIhKTCkKSmpkVmZmb2YjofTOzG81sk5lNiTF+qZl9vM39n5jZ3Ojtb5jZO2a2wcwu6sZr17X7+Jd4/owiJyot7AAiIZsK7HP3zWaWA/wSKAHOdPfdMcY/D5wLPBq9PwP4mZm9B7gSGBf9+JOZDXX3w5289l53HxCnn0UkrjSDkGQ3FVhuZsOBl4BqYHYH5QDwApGCwMwygWnAAmACUOnuB919OfB9IKsLr/3GSf8EIj1EBSHJ7gwgHXgZeMjdP+/uh44zfgkwxswKgDOBNe6+B1gEnGVm95jZEHef5+61XXhtFYQkLBWEJLupRP7vf6W7397ZYHdvIFImZxOZSTwffXxz9LFRwNtm9pkuvvaVZlbV5qM1g5lda2Zju/0TicSJabM+SVbRQ0R1wPuB/wX+y91/1oWv+w6QS2QGcIe7P9vu+YuB3wJnuPtbnbz2dHevOJmfQ6SnaAYhyWwi0AQsBi4FfmRms7vwdc8Ds4H3Rr8WM7upZdbg7k8BLwKTOnltB1Z1NMDMWr73q2Z2u5ktN7OvdSGfSFyoICSZnQG87u6N7v4aMAd4xMxO7eTrKoDTgDfdfX/0sXeAz5lZtpkNIlIOKzp57dXRQ1bHMLOBwO7o5wHAD4BZwIe7+LOJnDS9zVWS2VRgecsdd/+lmZUDT5rZ2W1++R/F3ZvMbGHbrwUeAMqB9UADcIO7r+3ktSeZWV3bbw0MdfdqYDKwMvr5t+5eG12P2NDtn1LkBGkNQiQBmdnXgc3ACGCLu883syuA/u5+T7jpJFnoEJNIYppEZAYxiSMzlTOij4kEQjMIERGJSTMIERGJSQUhIiIxqSBERCSmQN/mamYlwGPufm4n454Gvh/d9KxDAwcO9JEjR8YxoYhI37ds2bJ33b24s3GBFYSZFQEPAjmdjPtnYH1n5QAwcuRIKiq0S4GISHeY2eaujAvyEFMTcAVQ09EAM+sP/Cewz8xmBRVMRESOFVhBuHtN9AzR4/lXIhdiuQ+4Krrp2VHM7GozqzCzisrKyp6IKiIiJN4i9RnA3e6+E3gEmNl+QHSf/XJ3Ly8u7vQQmoiInKBEK4h1QFn0djmRrQZERCQEoRWEmc02s+vaPXwrcJ2ZLQHOI7IBmoiIhCDw3VzdfWb08wtEru/b9rntwIeCziQiIsdKtENMIiKSIJKyICo27eWOvxxvq34REUnKgnhp3bv811/e5s0dHZ6SISKS9JKyID579khyM9O4+8V1YUcREUlYSVkQhf0yuHL6CP6wagfrK+s6/wIRkSSUlAUB8IUZp5KZlsI9C9aHHUVEJCElbUEMzM3kU2cO54m/b2PL3gNhxxERSThJWxAAV59XRqoZ9y7ULEJEpL2kLojSgmw+Nm0oj1ZsZVdNfdhxREQSSlIXBMA154+iyZ15izaEHUVEJKEkfUEMH9CPS6YO4devbGZPXUPYcUREEkbSFwTAtTNH09DYzP0vbQw7iohIwlBBAKMH5fKhiaX8culmqg8cDjuOiEhCUEFEzZk1mrqGRh5cuinsKCIiCUEFEXX6kHwuGD+IB5ZsZH9DY9hxRERCp4JoY86s0VQdOMyvX9GF7EREVBBtnDG8iBmjBzJv0UbqDzeFHUdEJFQqiHaumz2ad+sa+N3ftoQdRUQkVCqIdt53an/eO7KIexeu51Bjc9hxRERCo4Jox8yYM2s0O6rreeLvW8OOIyISGhVEDOePLWbSKQXMXbCexibNIkQkOakgYjAzrps9ms17DvD7lTvCjiMiEopAC8LMSsxscRfGTTSzPweRqSMXji9hbEkud7+4juZmDzOKiEgoAisIMysCHgRyOhlnwO1AehC5OpKSElmLWLu7jufe2BlmFBGRUAQ5g2gCrgBqOhn3OeDFjp40s6vNrMLMKiorK+OZ7xgXTR7CqQNzuPOFdbhrFiEiySWwgnD3GnevPt4YMxsAfBq47TjfZ567l7t7eXFxcbxjHiU1xbjm/FGs3l7Dgrd7toxERBJNoi1S/wfwbXdPmC1VP3rGKZxSmM2dz6/VLEJEkkqiFcT5wC1mtgCYamY3hZyHjLQUvnJ+Ga+9U8XSDXvCjiMiEpjQCsLMZpvZdW0fc/ex7j7T3WcCy939e+GkO9rHy4dRnJfJXS+sCzuKiEhgAi+I6C9/3P0Fd7+rs3GJICs9lavPLeOv6/ewbPO+sOOIiAQi0Q4xJax/et9wivqlc/eLmkWISHJQQXRRTmYaX5hxKi+s2c3r2477ZiwRkT5BBdENV04fSV5mGnMXaBYhIn2fCqIbCrLT+czZI/nj6ztZu6s27DgiIj1KBdFNn59xKllpqcxdsD7sKCIiPUoF0U39czL49FnDeWrFdjbv2R92HBGRHqOCOAFfOreM1BTj3oWaRYhI36WCOAGD8rO4onwYjy3byvaqg2HHERHpESqIE/Tl88twh3mLNoQdRUSkR6ggTtDQon5cesYpPPzqO1TWNoQdR0Qk7lQQJ+GamaM43NTML17SLEJE+h4VxEkoK87loslD+NXSzVQdOBR2HBGRuFJBnKQ5s0az/1AT/7NkU9hRRETiSgVxksYNzuP9p5fwP0s2UlufMNc5EhE5aSqIOLhu9mhq6ht56OXNYUcREYkbFUQcTB5ayPlji7l/8UYOHmoKO46ISFyoIOLkutmj2bP/EA+/+k7YUURE4kIFESfvHdmf953an/sWraehUbMIEen9VBBx9NXZY9hV08Bjy7aGHUVE5KSpIOLonNEDmDKskHsWrOdwU3PYcURETooKIo7MjK/OGs3WfQd5avn2sOOIiJyUQAvCzErMbPFxnh9uZgvM7AUzm2dmFmS+ePiH8YMYX5rP3QvW0dTsYccRETlhgRWEmRUBDwI5xxn2ZeAad58NDAMmBZEtnsyM62aNZkPlfp59fWfYcURETliQM4gm4AqgpqMB7v5dd38zencA8G4QweLtAxMHU1acw50vrMVdswgR6Z0CKwh3r3H36q6MNbMrgNXufsyBfDO72swqzKyisrIy7jnjITXFmDNzNGt21vL8m7vDjiMickISbpHazMqAfwO+Hut5d5/n7uXuXl5cXBxsuG64eOoQhvXP5s4X12kWISK9UkIVRHSd4mHg812dbSSq9NQUvnL+KFZsqWLJuj1hxxER6bbQCsLMZpvZde0e/hYwHLgz+m6m80OIFjeXTxtKSX4md76wNuwoIiLdFnhBuPvM6OcX3P2uds9d7+6l7j4z+rEw6HzxlJmWypfPG8UrG/fyt017w44jItItCXWIqS/61JnDGZCTwV0vrAs7iohIt6ggelh2RipfOPdUFr5dycqtVWHHERHpMhVEAK48awT5WWmaRYhIr6KCCEBeVjqfO+dUnntjF2/trA07johIl6ggAvK5c0aSk5HK3S9qFiEivYMKIiCF/TL49PQR/H7ldjZU1oUdR0SkUyqIAH1xRhnpqSncs2B92FFERDqlgghQcV4mnzpzOE/8fRtb9x0IO46IyHGpIAJ29XllmMF9CzeEHUVE5LhUEAEbUpjN5dOG8ruKLeyuqQ87johIh1QQIbjm/NE0NTs/X6xZhIgkLhVECIYP6MfFU4bwq5ffYe/+Q2HHERGJSQURkmtnjqK+sYkHXtoYdhQRkZhUECEZU5LHBycO5sG/bqL64OGw44iIHEMFEaJrZ46mtqGRh5ZuCjuKiMgxVBAhmnhKAbNPG8T9L21kf0Nj2HFERI6iggjZnFmj2XfgML955Z2wo4iIHEUFEbJpI4o4Z/QA5i3eQP3hprDjiIi0UkEkgDmzRlNZ28CjFVvCjiIi0koFkQCmlw1g2ogi7l24gcNNzWHHEREBVBAJwcy4bvZotlUd5Im/bws7jogIoIJIGDPHFjPxlHzmvriOQ42aRYhI+AItCDMrMbPFx3k+3cyeNrMlZvb5ILOFzcz4xvvHsWnPAe7SVedEJAEEVhBmVgQ8COQcZ9hXgWXufg5wuZnlBRIuQcwaN4iPTh3C3BfX8cb2mrDjiEiSC3IG0QRcARzvN99M4JHo7UVAefsBZna1mVWYWUVlZWXcQ4btBx+ZQGG/dL752AotWItIqAIrCHevcffqToblAC2rtHuBkhjfZ567l7t7eXFxcbxjhq4oJ4MfXTKR1dtrmLdI24GLSHgSbZG6DsiO3s4l8fIF4oOTSvnwpFLu+Mta1u6qDTuOiCSpRPsFvAyYEb09BdgUXpRw3XDJBHIyU/nmYytpavaw44hIEgqtIMxstpld1+7hB4EbzOwO4HTgleCTJYaBuZn88OIJLN9SpWtGiEgoAi8Id58Z/fyCu9/V7rnNwIXAEuACd0/qzYkunjKEC8aXcNtzb7Ghsi7sOCKSZBLtEBPuvt3dH+nCgnafZ2b8+NKJZKalcP38lTTrUJOIBCjhCkKOVpKfxfcvOp2/bdrHQy9vDjuOiCQRFUQvcPm0oZw3tphbnl3Dlr0Hwo4jIklCBdELmBk/uWwSKWZcP38l7jrUJCI9TwXRS5xSmM23P3Qaf12/h4df1XUjRKTnqSB6kX86czhnjxrAzc+8yfaqg2HHEZE+TgXRi5gZ/3HZZJqanW8/vkqHmkSkR6kgepnhA/px/QfGsfDtSua/posLiUjPOaGCMLPfmtlD0Y9b4x1Kju+q6SMpH1HEjU+vZndNfdhxRKSPOtEZxFJ3v9LdrwRuiWcg6VxKinHr5ZNpaGzmu0++rkNNItIjTrQgLjGzr5rZWHffE9dE0iVlxbl84/1j+fMbu3h65Y6w44hIH3SiBXElsB74mJn9Io55pBu+MKOMKcMK+cH/vc67dQ1hxxGRPqbbBWFmNwLXErm4z2Pu/sW4p5IuSU0xfnr5ZPY3NPGDp1aHHUdE+phOC8LMJrS97+7/Dvw3UEtkBvHzHsomXTC2JI+v/cNo/rByB8++rkNNIhI/XZlBPNRyw8y+CODuu9z9WeC/3f1LPRVOuubL549iwpB8vvfkavbtPxR2HBHpI7pSENbm9rXtnlscxyxygtJTU7j18slUHTjEj37/RthxRKSP6EpBtH0PpbV7TifaJYgJQwq4duYoHv/7Nl5YsyvsOCLSB3TlF/xgM/usmZ3BsQWhN+AnkOtmj2FcSR7ffnwV1QcPhx1HRHq5rhTED4Fy4GfAUDNbbWbzzezHwMCeDCfdk5EWOdRUWdvAzX94M+w4ItLLpXU2wN3ntb1vZkOBycAkYFEP5ZITNGVYIVefN4p7F67noimlnDumOOxIItJLdXsNwd23uvsz7n6Lu3+6J0LJyfn6BWMoK87hW/NXUdfQGHYcEemltMjcB2Wlp/LTyyezvfogt/xxTdhxRKSXCqwgzOx+M1tqZt/r4PkiM3vGzCrM7L6gcvVV00b053Nnn8pDL2/m5Q3aLktEui+QgjCzy4BUd58OlJnZmBjDrgR+7e7lQJ6ZlQeRrS/7t38cy/D+/bh+/koOHmoKO46I9DJBzSBmAo9Ebz8HzIgxZg8w0cwKgWFAzAsvm9nV0VlGRWVlZU9k7TP6ZaRxy8cms3nPAW577q2w44hILxNUQeQALZc/2wuUxBjzEjAC+BrwZnTcMdx9nruXu3t5cbHeodOZ6aMG8OmzhvPAko0s2xzzj1REJKagCqIOyI7ezu3gdX8AfMXdbwTWAJ8LKFuf960PjmdIQTbffGwl9Yd1qElEuiaogljGkcNKU4BNMcYUAZPMLBV4HzpLO25yM9P4yWWT2FC5nzueXxt2HBHpJYIqiCeBK83sduATwGozu6ndmJ8A84BqoD/wcEDZksJ5Y4u5onwY8xZtYOXWqrDjiEgvEEhBuHsNkYXql4FZ7r7C3b/Xbsyr7j7B3XPd/UJ3rwsiWzL5zofHMzA3g28+upJDjc1hxxGRBBfYeRDuvs/dH3H3nUG9phytIDudmy+dxFu7arnrxXVhxxGRBKczqZPMP4wv4dIzTmHui+t4Y3tN2HFEJIGpIJLQv190OoX9MvjmYys43KRDTSISmwoiCRXlZHDTRyewensN8xZtCDuOiCQoFUSS+sDEUj48qZQ7/rKWtbtqw44jIglIBZHEbrhkAjmZqXzzsZU0Neu0ExE5mgoiiQ3MzeSHF09g+ZYqHnhpY9hxRCTBqCCS3MVThnDB+BJue+4tNlTq1BMROUIFkeTMjB9fOpHMtBSun7+SZh1qEpEoFYRQkp/F9y86nb9t2sdDL28OO46IJAgVhABw+bShnD+2mFueXcOWvQfCjiMiCUAFIUDkUNNPLptEihnXz1+Juw41iSQ7FYS0GlKYzXc+NJ6/rt/Dw6/GvKCfiCQRFYQc5VNnDuPsUQO4+Zk32V51MOw4IhIiFYQcxcz4j8sm09TsfPvxVTrUJJLEVBByjOED+nH9B8ax8O1K5r+2rfMvEJE+SQUhMV01fSTvHVnEjU+vZndNfdhxRCQEKgiJKSXFuOVjk2lobOa7T76uQ00iSUgFIR0qK87lG+8fy5/f2MXTK3eEHUdEAqaCkOP6wowypgwr5N//73VWbKkKO46IBEgFIceVmmLcccVUcjPTuGLeUp5ZpZmESLIIrCDM7H4zW2pm3+tk3Fwz+0hQuaRzIwfm8OScczi9NJ9rf/0ad7+4TmsSIkkgkIIws8uAVHefDpSZ2ZgOxp0LDHb3p4PIJV03MDeT33zpLC6eMoSf/ukt/u3RlTQ0NoUdS0R6UFAziJnAI9HbzwEz2g8ws3Tg58AmM7uko29kZlebWYWZVVRWVvZEVulAVnoqd3xyKv96wVjmv7aVK3/xKnv3Hwo7loj0kKAKIgdoOeNqL1ASY8xVwBvArcCZZvbVWN/I3ee5e7m7lxcXF/dIWOmYmfEvF4zhvz91Bsu3VnHp3CWs260LDYn0RUEVRB2QHb2d28HrngHMc/edwK+AWQFlkxNw8ZQhPPyls9jf0Mhlc5ewZN27YUcSkTgLqiCWceSw0hRgU4wx64Cy6O1yQFeuSXDTRhTxxLXnMLggi6seeJXfvPJO2JFEJI6CKogngSvN7HbgE8BqM7up3Zj7gVlmtgi4FrgtoGxyEob178f8a85mxuiBfOeJVdz0+zdo0mVLRfoEC+rtimZWBFwILIoeRjpp5eXlXlFREY9vJSepsamZH/3+DR5cupkLxpdwxyenkpOZFnYsEYnBzJa5e3ln4wI7D8Ld97n7I/EqB0ksaakp3HDJRG64eAIvrNnF5fcu1fUkRHo5nUktcfWZs0fywGffy5a9B/jo3UtYuVXbc4j0VioIibuZ4wYx/5qzyUhL4RP3LeWP2p5DpFdSQUiPGDc4r3V7jmu0PYdIr6SCkB4Ta3uOQ43NYccSkS7S20ykR7Vsz1FWnMPP/rKWLfsOcO+np9E/JyPsaCLSCc0gpMeZGV+/YCx3fHIqy7dEtudYX6ntOUQSnQpCAnPJ1FN4+EtnUVffyKV3L+Gv2p5DJKGpICRQ00YU8eScI9tz/PZVbc8hkqhUEBK4lu05zhk9kG89voof/0Hbc4gkIhWEhCIvK537P1POZ6aP4OeLN/Llh5axv6Ex7Fgi0oYKQkLTfnuOj9+7lB3V2p5DJFGoICR0LdtzvLP3AJfcpe05RBKFCkISQsv2HOmpke05nn1d23OIhE0FIQmjZXuO8aX5fOVXrzF3gbbnEAmTCkISSnFeJg9Ht+e49dm3+OZj2p5DJCzaakMSTsv2HKcOzOGO59fyzt4D3PfpaRRpew6RQGkGIQnJzPjXC7U9h0iYVBCS0CLbc7yP2pbtOdZrew6RoKggJOFNG9GfJ+ecQ0l+Flfdr+05RIKigpBeYVj/fsy/9mzOjm7PcfMzb2p7DpEepoKQXiM/K50HPlPOVdNHMG/RBr7yK23PIdKTAisIM7vfzJaa2fc6GVdiZn8PKpf0LmmpKdx4yUR++JHTef7NXVxy9xJu+9NbPLd6J7tr6sOOJ9KnBPI2VzO7DEh19+lm9oCZjXH3tR0Mvw3IDiKX9F6fPedURg7M4ad/eot7Fq5vPdxUWpDFlKGFTBlWyJShBUwaWkBeVnrIaUV6p6DOg5gJPBK9/RwwAzimIMxsNrAf2NnRNzKzq4GrAYYPHx7vnNKLzBw3iJnjBnHwUBNv7Khm+ZZqVmypYsXWKp5dHflPyAxGFedGS6OAKUMLOa00j8y01JDTiyS+oAoiB9gWvb0XeE/7AWaWAXwfuBR4sqNv5O7zgHkA5eXlWqUUsjNSmTaiP9NG9G99bN/+Q6zcFimMlVurWPj2bua/thWAjNQUxg/JZ8rQgtbZRtnAHFJSLKwfQSQhBVUQdRw5bJRL7LWPbwFz3b3KTP9Q5eQU5WRw/thizh9bDIC7s726vnWGsWJLFfOXbeWXSzcDkJeZxqShBdFDU4VMHVbI4IKsMH8EkdAFVRDLiBxWehmYArwVY8wFwGwzmwNMNbNfuPsXA8onfZyZcUphNqcUZvOhSaUANDU7GyrrWN5aGtX8fNEGGqPrGYPyMpkyLFIWU4YWMmloAQXZWs+Q5GFB7JZpZvnAYuB54IPAJ4GPu3vMdzSZ2QJ3n9nZ9y0vL/eKiop4RpUkV3+4iTd31ERnGtWs2FrFhsr9rc+XDcxpXQCfPKyQ00vzyUrXeob0Lma2zN3LOx0X1HbKZlYEXAgscvcOF6G7QwUhQag+eJhV0bJYsaWK5Vuq2F3bAEBaijG+NJ8pwwqYHD00Nao4l1StZ0gCS7iC6AkqCAnLzur61sJYsbWKlVuqqY2etJeTkcqEUwoYW5LL6OJcRg/KY/SgXEryM9H6miSCrhaEtvsWOQGDC7IYXDCYf5wwGIDmZmfjnv2RwthSxapt1Ty1fDs19UfO9M7LTKNsUEtpHPkY3r+fZhySkDSDEOkh7k5lXQPrdtexfncd63bXsa4y8nlXTUPruIzUFMqKcxjVrjxOHZij9Q3pEZpBiITMzBiUl8WgvCzOHjXwqOdq6g9HCqNNeby+rZo/rtpByx6EKRbZpLClNEa1mXXk6+xwCYAKQiQE+VnpvGd4Ee8ZXnTU4/WHm9j47v7W8mj5WLz2XQ41Hbn06qC8zKMOU7V8FOdqnUPiRwUhkkCy0lMZX5rP+NL8ox5vbGpmy76DRxdHZR2Pv7aNujY72uZnpR1bHMV5DC3K1pni0m1agxDpxdydXTWRdY61u2uPHLaqrOPdukOt4zLTUigrzmXMoFzGDc5jfGke4wbnM6QgSzOOJKQ1CJEkYGbRd1RlMWPM0escVQcOHTPjWLZ5H0+t2N46Ji8rjfGD8zmtNI9xg/M4bXA+4wbnkZupXw2ighDpswr7ZVA+sj/lI/sf9XhN/WHe3lnLmztrWbOjhjU7a485VDW8f7/ITGNwHqeVRkpj5IAcvR03yaggRJJMflb6McXh7mzdd5A1LaWxK/L5+Td3tb6rKis9hbEleZw2OHJ4qqU8+udkhPSTSE/TGoSIdKj+cBNrd9WxZmdkprFmZw1rdtSyZ/+R9Y1BeZnRdY18Tosepho1KEfX3EhgWoMQkZOWlZ7KpOiV+dqqrG1oLYuW4vjfJZta34qblmKUFee0rmmML40UR6kWxXsVFYSIdFtxXibFecWcO6a49bHGpmY2vrv/qJlG+0Xx/Kw0Tosuird8HleSR44WxROS/lZEJC7SUlMYU5LHmJI8PjJlSOvj1QcP8/auIwvia3bWMn/ZVvYfamodM7QomyGF2ZTkZ1GSl8mg/ExK8iNnoZdEb6tEgqc/cRHpUQXZ6bx3ZH/e22ZRvLnZ2VZ1ZFH87d117KqpZ9XWKv5cU0/94eZjvk9uZhqD8jMZlBcpjEiBHLldkp/JoLwssjO09hEvKggRCVxKijGsfz+G9e/HhaeXHPWcu1Pb0Mjumnp21TSwuzbyeVdNPbujn197Zx+7aho41HhskeRlpbUWRkleFoPalEfLbKQ4L1MbIXaBCkJEEoqZkZ+VTn5WOqMH5XU4zt2pOdjIrtp6dtW0LZEjxfLKxr3srq3ncNOx79Ys7JceLZCjy6MkPzNaKlkU52aSkZbSkz9uQlNBiEivZGYU9EunoF86Y0uOXyT7DhyOlkg9u2sbWktkV009u2obWLf7XXbXNtDUfGyRDMzNYHBBFqUF2ZRGz1ovLchicP6R+311NqKCEJE+zczon5NB/5yMYzZBbKu52dl74NBRh7J2RktlR3U9W/Ye4NWNe6k+ePiYry3ql87gaIG0fAxuVyj9Mnrfr9vel1hEpAekpBgDczMZmJvJhCEdjztwqJGd1fXsrI4Ux86aerZXHWy9v3xLFXvbnEjYIj8rjdKC7CMzkIIshrS7n5dg1/lQQYiIdEO/jDTKinMpK87tcEz94abWmUdrkVQfbC2UN3bUUFnbcMzX5WamtTmE1WYmUhidmeRnk5+dFtjJhoEVhJndD5wO/MHdb4rxfAHwWyAV2A9c4e7H1rCISILLSk9lxIAcRgzI6XDMocbm1sNYRxVItFDW7nqX3bX1tF8WyU5PpbQgi+9/5HRmjRvUoz9HIAVhZpcBqe4+3cweMLMx7r623bB/Bm539z+b2T3AB4CngsgnIhK0jLSU1rf6dqSxqZnKuoajimNH1UF21NRT1K/nN0kMagYxE3gkevs5YAZwVEG4+9w2d4uB3bG+kZldDVwNMHz48HjnFBFJGGmpKdF3T2WH8vpBvcE3B9gWvb0XKOlooJlNB4rc/eVYz7v7PHcvd/fy4uLiWENERCQOgppB1AEtFZhLB8VkZv2BO4GPBZRLREQ6ENQMYhmRw0oAU4BN7QeYWQbbpsAIAAAExElEQVTwKPBtd98cUC4REelAUAXxJHClmd0OfAJYbWbt38n0BeA9wHfNbIGZXRFQNhERiSGQQ0zuXmNmM4ELgVvdfSewot2Ye4B7gsgjIiKdC+w8CHffx5F3MomISIJL3m0KRUTkuFQQIiISk7kfu71tb2FmlcCJvuNpIPBuHOPEi3J1j3J1j3J1X6JmO5lcI9y90xPJenVBnAwzq3D38rBztKdc3aNc3aNc3Zeo2YLIpUNMIiISkwpCRERiSuaCmBd2gA4oV/coV/coV/clarYez5W0axAiInJ8yTyDEBGR41BBSKfMrL+ZXWhmA8POIiLBSdqCMLMSM1scdo4WZlZgZn80s+fM7Ino7rahM7Mi4PfAmcCLZpZQF+GI/j3+PewcLcwszczeiW44ucDMJoWdqS0zm2tmHwk7Rwszu6bNn9VyM7sv7EwQ+e/ezJ4xs4pEyQRgZqea2R/MbLGZ/WdPv15SFkT0l96DRC5klChaLrn6fmAnkUuuJoLJwP9z9x8DfyKy424iuY0j1xpJBJOBh919ZvRjVdiBWpjZucBgd3867Cwt3P2elj8rYDHw85AjtbgS+HX0PIM8M0uU8yBuAX7k7ucCQ6OboPaYpCwIoAm4AqgJO0gLd5/r7n+O3u3wkqtBc/eF7v6ymZ1HZBaxNOxMLcxsNrCfSKEmirOAi8zsVTO738wC2xDzeMwsncgv301mdknYedozs1OAEnevCDtL1B5gopkVAsOALSHnaTEWeC16ezdQ0JMvlpQF4e417l4ddo5YOrvkahjMzIgU6j7gcMhxgNYLTH0f+FbYWdr5G3CBu58JpAMfCjlPi6uAN4BbgTPN7Ksh52lvDom13f9LwAjga8CbRC6VnAgeA34QPUz4AeD5nnyxpCyIRNXmkqufDztLWx4xB1gJXBx2nqhvAXPdvSrsIO2sdPcd0dsVwJgww7RxBjAvei2WXwGzQs7TysxSiORZEHKUtn4AfMXdbwTWAJ8LOQ8A7n4T8Efgi8CD7l7Xk6+ngkgQiXrJVTO73syuit4tBBLlF/IFwBwzWwBMNbNfhJynxUNmNsXMUoGP0u7CWCFaB5RFb5dz4ptc9oRzgVc8sU7KKgImRf8e3wckUrblwHDg9p5+oaQ+Uc7MFkQXx0JnZtcAN3PkF8o97v67ECMBrQv6jwCZwOvAnAT7h5xof48Tgd8ABjzl7t8NORIAZpYHPACUEDn0dbm7bws3VYSZ3QxUuPvjYWdpYWZnAv9D5DDTUuDSnv6/9a4ysxuAde7+UI+/VoL9WxcRkQShQ0wiIhKTCkJERGJSQYiISEwqCBERiUkFISIiMakgREQkJhWESByZ2ZfN7N7o7XQze8jMHozuhSTSq6ggROJrMrDSzPKJbInwjrt/xt0TYg8rke5QQYjE1yQiG7stAB5NlDOpRU6EzqQWiSMz2wc0Ap9PpOsuiJyIhNirXqQvMLNhQB2wFigNOY7ISVNBiMTPZCKbLX4JeNnM/ubuCXM5VJHu0hqESPxMAlZFrwfxReB3ZtajV/wS6UkqCJH4mQSsAohePvYRIltsi/RKWqQWEZGYNIMQEZGYVBAiIhKTCkJERGJSQYiISEwqCBERiUkFISIiMakgREQkpv8PDxQvxhjM2cAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "\"\"\"\n",
    "Created on Tue Apr 30 11:27:42 2019\n",
    "\n",
    "@author: qinzhen\n",
    "\"\"\"\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import helper as hlp\n",
    "\n",
    "#### (a)\n",
    "n = 1000\n",
    "X, y = hlp.Data(n, scale=0.5) \n",
    "plt.scatter(X[:, 0], X[:, 1], edgecolor='k', c=y)\n",
    "plt.show()\n",
    "\n",
    "n = X.shape[0]\n",
    "K = np.arange(1, 10)\n",
    "Ein = []\n",
    "for k in K:\n",
    "    #训练模型\n",
    "    kmeans = hlp.KMeans_(k)\n",
    "    kmeans.fit(X)\n",
    "    #获得标签\n",
    "    label = kmeans.labels_\n",
    "    #获得聚类中心\n",
    "    center = kmeans.cluster_centers_\n",
    "    #计算Ein\n",
    "    ein = 0\n",
    "    for i in range(k):\n",
    "        #计算每一类的误差\n",
    "        ein += np.sum((X[label==i] - center[i]) ** 2)\n",
    "    #计算均值\n",
    "    ein /= n\n",
    "    Ein.append(ein)\n",
    "\n",
    "#作图\n",
    "plt.plot(K, Ein)\n",
    "plt.title(\"$K$ VS $E_{in}$\")\n",
    "plt.xlabel(\"$K$\")\n",
    "plt.ylabel(\"$E_{in}$\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### (b)\n",
    "#记录结果\n",
    "Ein_rand = []\n",
    "#试验次数\n",
    "N = 1000\n",
    "\n",
    "for k in K:\n",
    "    ein_k = []\n",
    "    for _ in range(N):\n",
    "        X, y = hlp.Data(n, scale=0.5) \n",
    "        #计算范围\n",
    "        X1_min = np.min(X[:, 0])\n",
    "        X1_max = np.max(X[:, 0])\n",
    "        X2_min = np.min(X[:, 1])\n",
    "        X2_max = np.max(X[:, 1])\n",
    "        #生成点\n",
    "        X1_rand = np.random.uniform(X1_min, X1_max, size=n)\n",
    "        X2_rand = np.random.uniform(X2_min, X2_max, size=n)\n",
    "        #合并\n",
    "        Xrand = np.c_[X1_rand, X2_rand]\n",
    "        #训练模型\n",
    "        kmeans = hlp.KMeans_(k)\n",
    "        kmeans.fit(Xrand)\n",
    "        #获得标签\n",
    "        label = kmeans.labels_\n",
    "        #获得聚类中心\n",
    "        center = kmeans.cluster_centers_\n",
    "        #计算Ein\n",
    "        ein = 0\n",
    "        for i in range(k):\n",
    "            #计算每一类的误差\n",
    "            ein += np.sum((Xrand[label==i] - center[i]) ** 2)\n",
    "        #计算均值\n",
    "        ein /= n\n",
    "        #存储结果\n",
    "        ein_k.append(ein)\n",
    "    Ein_rand.append(np.mean(ein_k))\n",
    "    \n",
    "plt.plot(K, Ein_rand)\n",
    "plt.title(\"$K$ VS $E^{{rand}}_{{in}} (k)$\")\n",
    "plt.xlabel(\"$K$\")\n",
    "plt.ylabel(\"$E^{{rand}}_{{in}} (k)$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAEYCAYAAACdnstHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAIABJREFUeJzt3Xl8FeXZ//HPlQUSIECAsO+byL4EBBUFi4oUHxUXXIq21uLCr9RH26qPtj4urdUqrbWKUpcqj6K4oXVFVBQUhSBhB9n3JRC2sC/X748zkRgSEkJyJsv3/XrlxZw598xcA3q+uWfuc4+5OyIiIkURE3YBIiJSdilERESkyBQiIiJSZAoREREpMoWIiIgUmUJERESKTCEiIiJFphAREZEiU4iIlFFm9pCZ3Zrj9Roz65ZHu+lm1iG61UlFoRARycXMks3MzaxZ8NrM7H4zW2lmXfJoP83MLs/x+iEzeypYvt3MVpvZcjMbXMjjJ5rZfWY228y2mdkqM3vdzHrnaJMCXAs8k10z0ABYmMcuHwXuL/zfgEjhKUREjtUV2Obuq8ysKvAGcA7Qy91n59H+U6BvjtdnAp+aWXdgGHAKMAR4zszij3fg4HifAD2Aq9w9GegQrDsvR9OfAx+4+97gdSdgqbvvy2O37wL9zazB8Y4tUhQKEZFjdQXSzawpMBXYAZzj7pvzaf8ZQYiYWWUiATCZyId/hrvvdfd04A9AQgHH/gtgwMXuvgDA3bPcfYy75+xNXAB8keN1Z2BeUEMVM3vFzN4ys2pBsMzkxyEkUiwUIiLH6gbEA98AY939enc/cJz2XwFtzKwG0AtY5O5bgS+B3mY22swaBkGwK7+dmFkt4EbgTnc/VECNnYDFOV53BuaaWQsiwbcYuNTds4L3FwLHXIoTOVkKEZFjdSXSi5jj7qMKauzu+4kEzulEeiSfButXBetaAd+b2XUF7OocINPdp2SvCG6KbzezvWZ2Vo62NYGcgdSJyD2Rz4D73P0+//EU3buCbUSKlUJEJIfgctSpwKXAqTlHPxUg+5LWDyEC4O5z3f084GpgtJmdcpx91AfW51zh7r2ANkQug83L8dY2ICmo2YCOwCXA0+7+Th77TgK2F/JcRApNISLyYx2Bw8AUIh/KD5jZOYXY7lMiPYmewbaY2YPZvQ93fxf4nEiPIT+rgSZmFptrfVdgjbtn5lg3B2gbLLcI/hwA3G5mqXns+1Qgr0EBIidFISLyY92Aee5+yN2/A0YA44N7DceTBrQDFrr77mDdauAXwZDdukQC5Hgf5JOIXHb6u5nVCoYWtwCuz2O7D4Czg+XORC69zQWGA2/nHImV42b/JwWcg8gJU4iI/FhXID37hbu/BLwCTAiG3+bJ3Q8TGS31WY7VzwPfA8uAb4ncq1hynH3sAc4FGgOLgAzgbWA5kTDL6SVgkJklEgmnOcE+JgBjgnqzR4L9FzDZ3dcjUsxMj8cVKZvM7M/AZnf/ewHtvgV+6e7zjtdOpCgUIiIiUmS6nCUiIkWmEBERkSJTiIiISJHFRetAZvYc0B54390fzOP9FsA/gerAdHe/PZhG4lUgFtgNDAWOEBmtsjzY9NfB0MY81alTx5s3b16cpyIiUu7NnDlzi7unFNQuKiFiZkOAWHfvY2bPm1mbPIY6Pgw84O7fmNlrZtaPSOiMcvdPzGw0MBBYC4xz9zsKc+zmzZuTlpZWjGcjIlL+mdmqwrSL1uWsfsD4YHkikamyc2sLfBcsbwZquPtT7p79BamUYH1vYHAwp9BzZnZMEJrZcDNLM7O0jIyM4jwPERHJIVohUhVYFyxnAvXyaPMGcK+ZXUikx/HD/ENm1gdIdvdvgBnAgGBOoXhgUO4dBbOlprp7akpKgb0xEREpomjdE8kCEoPlauQRXu7+oJmdCfwOeDF7CutgeuwniEyIB5HpHfYHy2lEJqcTEZEQRKsnMpOjl7C6ACvzaZcONAVGAZhZJeB14K5gWm2AsWbWJZik7mI0qZyISGiiFSITgGFmNgq4AphvZseM0CLSCxkVzCEE8EugO3C3mU02s6FEnhU9lkjgTHP3SSVfvoiI5CVq056YWTKRyeW+dPeNUTkokJqa6hqdJSJyYsxsprvn9ViBH4na90TcfRtHR2iJiEg5oG+s52NL1n7u+898duw5GHYpIiKllkIkH5t27uPfX6/kH5/l+/gHEZEKTyGSjw4NazA0tQkvfr2S5RlZYZcjIlIqKUSO4/bzTiEhPpY/f7Aw7FJEREolhchxpCRVZkT/1kxauJkpSzR9iohIbgqRAvzijOY0qZXIg+8t5NDhI2GXIyJSqihECpAQH8v/XHAqizft4tUZa8IuR0SkVFGIFMLAjvXp1aIWoz75nh17NeRXRCSbQqQQzIw/Dm7Ptj0HeOJTDfkVEcmmECmkjo1qcEWPJvxbQ35FRH6gEDkBt5/flspxMfz5g0VhlyIiUiooRE5A3aQERpzTmkkLNzF1yZawyxERCZ1C5ARdf0YLGicn8sB7CzTkV0QqPIXICUqIj+V/BkWG/L6WpiG/IlKxKUSK4IKO9enVvBaPTfyenfs05FdEKi6FSBGYGX+8MDLk95+fLQ27HBGR0EQtRMzsOTObZmb35PN+CzN738ymmNljx9uuoH1FQ8dGNbi8R2Ne+GoFK7fsDqsMEZFQRSVEzGwIEOvufYCWZtYmj2YPAw+4e1+gsZn1y2u7Qu4rKn573ilUio3hT5rlV0QqqGj1RPpx9NG4E4Ez82jTFvguWN4M1MhnuwL3ZWbDzSzNzNIyMkpu9t261RO4pX9rPlmwia+WasiviFQ80QqRqsC6YDkTqJdHmzeAe83sQmAg8Gk+2xW4L3cf4+6p7p6akpJSbCeRl1+e2YJGNSNDfg8f8RI9lohIaROtEMkCEoPlankd190fBD4EbgBedPesfLYrcF/RlD3kd9HGXbymWX5FpIKJ1gfwTI5eduoCrMynXTrQFBh1nO0Ku6+oGdSpPj2bJ/PYxMUa8isiFUq0QmQCMMzMRgFXAPPN7ME82v0OGOXue/LZ7v181oUqMstvBzL3HOBJDfkVkQokKiHi7juJ3BD/Bujv7rPd/Zjhue5+r7uPPc52O/JaV/JnULBOjWtwaffGPK8hvyJSgUTtfoK7b3P38e6+8WS3K+q+Strvzz+F+NgYHvpQQ35FpGLQN9aLUd3qCYzo35qP52/i62Ua8isi5Z9CpJhlD/m9/z8a8isi5Z9CpJglxMdy16B2LNq4i/Ga5VdEyjmFSAn4aacGpDZL5tGPNeRXRMo3hUgJyJ7ld+vuAzz5uYb8ikj5pRApIZ0b1+TS7o15YepKVm3VkF8RKZ8UIiXo9wNPIS7WeOiDRWGXIiJSIhQiJahe9QRu6deKj+ZvZNqyrWGXIyJS7BQiJeyGvi01y6+IlFsKkRKWEB/LnRe0Y8GGnbyuIb8iUs4oRKJgcOcG9GiWzKMTF7NLQ35FpBxRiERBZJbf9mzJOsCTny8LuxwRkWKjEImSLk1qMqR7I56fuoLVW/cUvIGISBmgEImi35/fjtgY0yy/IlJuKESiqH6NBG7u14oP523km+Xla8jvzn0HeeaLZXy+aLNGoYlUIHHROpCZPQe0B94Pnqee+/1k4GWgLjDT3W80s5uBoUGTmsC3wAhgefAD8Gt3n1vS9ReX4We15NXpq3ngvQW8+//OJDbGwi7ppH23ehsjx81i7ba9ADSqmcjQnk24IrUJ9WskhFydiJSkqPREzGwIEOvufYCWZtYmj2bDgJfdPRVIMrNUdx/t7v3cvR8wBfgX0BkYl72+LAUIBEN+B53K/PU7eXPm2rDLOSlHjjhPfr6Uy5+ehju8Nrw3T13TnRZ1qjLqk+854+HP+NVLaeqdiJRj0eqJ9APGB8sTgTOBJbnabAU6mllNoAnww5cqzKwRUM/d08zsFmCwmfUH5gI3uvuhnDsys+HAcICmTZsW/9mcpAs7N+DfX63gkY8XM6hzA6pVjlqHsNhs2rmP28an89XSrfy0cwP+fEknaiTGAzCoUwNWbd3NqzPW8HraGj5ZsEm9E5FyKlr3RKoC64LlTKBeHm2mAs2AkcDCoF22EcDoYHkGMMDdewHxwKDcO3L3Me6e6u6pKSkpxXMGxSgyy28HtmTtL5Oz/H62aBMXPD6Fmau28fClnfjnVd1+CJBszWpX5Y6B7fj6zp/w1DXdaZkS6Z2c/pdPueHFND5btEm9E5FyIFq/AmcBicFyNfIOr3uBm9x9p5ndBvwCGGNmMUB/4O6g3Rx33x8spwF5XRor9bo2qcmQbo14bsoKru7VlCa1qoRdUoH2HzrMwx8u5vmvVtCufhL/vLo3resmHXebSnExDOrU4JjeyaSFm2hYI4GhPZsytKd6JyJlVbR6IjOJXMIC6AKszKNNMtDJzGKB04DsX1P7At+6e/brsWbWJWh3MTC7xKouYb8beEqZGfK7PCOLIU99zfNfreC6Ps2YMOKMAgMkt5y9k9HXdKdV3Wr8bZJ6JyJlWbR6IhOAKWbWELgAuNLMHnT3e3K0eQh4gcglrWnAuGD9+cCXOdrdD7wCGPCuu08q6eJLSoMaidx0div+Nul7vl2+ldNa1g67pGO4O2/MXMu9786nUlwM/7o2lXPb53U1svAqxcVwQacGXNCpAau37mHcjNXH9E6u6NmYBjUSC96ZiITKjv6CX8IHigzhPRf40t03RuWgQGpqqqelpUXrcCds74HD/OSxySRXrVTqhvzu2neQeybM45309ZzWohZ/v7JriX2wHzh0hE8XbuKV6auZsmQLMQbntKvL1ac15ey2dUvV34tIRWBmM4PRssdvF60QCUtpDxGAd9LX8ZtX03nkss5ckdok7HIASF+zPfjuxx5uHdCWEf1bR+2DfPXWPbw6YzXj09ayJWs/DWskcEXPJgzt2US9E5EoUYgEykKIuDtDRn/N2m17+fy3/UId8nvkiDNmynIe/Xgx9aon8PiVXUltXiuUWg4ePsKkBcf2Tq7q1ZR+p6h3IlKSFCKBshAiALNWb+OSp75mRP9W/O78dqHUsHnXPm4fP5spS7YwsEN9Hr60MzWqxBe8YRSs3rqH19IivZOMXftpUCPhh++dNKyp3olIcVOIBMpKiAD892vpvD93A5/ednbUh/x+8X0Gt49PZ9e+Q/zxwvZc3aspZqXvN/2DhyP3Tl7+9mjvpP8pkXsn6p2IFB+FSKAshciGHXvp/+hkftKuHk9e0z0qxzxw6AiPTlzMmC+X07ZeNf55dXfa1juxobthWZN59N5Jdu/kitTIvRP1TkROjkIkUJZCBODvk77n75OWMP7GPvRqUbL3IlZu2c3IV2cxZ+0OrjmtKX8Y3J6E+NgSPWZJyO6dvDJ9DVOWZGBEeieReycpxMVqsmqRE6UQCZS1ENl74DDnPDaZ2tUq8e6IM4kpocszE2at4+635xIbYzxyWWcGdmxQIseJtvx6J9ef2eKYqVlEJH+FDRH9ilbKJFaK5Y6B7Zi3bidvflf8s/xm7T/EbePTufW1dNo3rM6Ht55VbgIEoEmtKvzu/HZ8fec5PP2zHrSpl8Q/PlvCkKe+Yk2mnigpUtwUIqXQRV0b0q1pTR75eDG79x8qeINCmrt2Bxc+MZUJs9bxm5+0YdyvetOonN47iI+NYWDH+rx0fS/G/ao3W7IOcMlTX5G+ZnvYpYmUKwqRUsjM+MPg9mTs2s/oyctOen9HjjjPTlnOkNFfsffAYV75VW/++9y2FeZeQe+WtXnz5tNJrBTLlWOm8fH8qE2YIFLuVYxPkTKoe9NkLu7akDFTlrN2W9Evw2zJ2s/1L87gwfcX0u+Uunz4m770LoVzdJW01nWr8fYtZ9CufnVu+r+ZPDd1BeX9fqBINChESrHfD2xHjMFfPlxUpO2nLtnCBY9P4etlW7n/og6MGdaD5KqVirnKsqNOtcq8Orw3AzvU54H3FvC/787XrMEiJ0khUoo1rJnIjWe14r05G0hbmVnwBoGDh4/w8EeLGPb8t9RIjOedEWdwbZ/mpfLLg9GWEB/Lk1d3Z/hZLXlx2iqGv5RWrPedRCoahUgpd+PZLalfPYH7/rOAI4X4rXlN5h4uf3oaoycv48qeTXj3/53BqQ2qR6HSsiMmxvifQafywEUd+HzxZoaOmcbmnfvCLkukTFKIlHJVKsVxxwWnMHfdDt6ate64bd+dvZ5Bj09hWUYW/7y6Gw8N6UyVSmXv+e3RMqxPc569LpXlGbu5+MmvWLxxV9gliZQ5CpEy4KIujejSpCaPfLQoz0svew4c4vdvzGbkuFm0qVeND0b2ZXDnhiFUWvac064e42/sw6EjzmWjv2bqki1hlyRSpihEyoCYGOPeC9uzedd+nv7ix0N+56/fweAnpvL6zLWM6N+K127sUyae116adGxUgwkjzqBRciI/f2E642esCbskkTIjaiFiZs+Z2TQzuyef95PN7AMzSzOzZ4J1cWa22swmBz+dgvX3mdkMM3syWvWHrXvTZC7q2pAxX0aG/Lo7L3y1gkue/JqsfYd4+Zen8bvz2xFfQb77Udwa1kzk9Zv6cHrrOvz+zTk8+vFiDQEWKYSofOKY2RAg1t37AC3NrE0ezYYBLwdztSSZWSrQGRjn7v2Cn7lm1gM4E+gFbDazAdE4h9LgjoHtMIP/fXcBv3opjfv+s4C+berw0a1ncXrrOmGXV+YlJcTz3HWpXNWrCf/8fCm/eTWd/YcOh12WSKkWrV9b+wHjg+WJREIgt61ARzOrCTQB1gC9gcFmNj3oycQBZwNveuTXxI+Bvrl3ZGbDgx5NWkZGRvGfTUga1kxk+FmtmLRwE19+v4U/Dm7Ps9elUqsCf/ejuMXHxvDnSzpxx8B2vDt7PcOenc623QfCLkuk1IpWiFQFsocWZQL18mgzFWgGjAQWBu1mAAPcvRcQDwwqzL7cfYy7p7p7akpKSnGeR+huOrslN53dirduOZ3rz2yh736UADPj5n6teOKqbqSv3c6lo79m1dbdYZclUipFK0SygOyZ/qrlc9x7gZvc/X5gEfALYI67bwjeTwPaFHJf5VaVSnHceUE7OjaqEXYp5d6FXRryyg2nsW3PAS556mtmrtoWdkkipU60PoBncvQSVhdgZR5tkoFOZhYLnAY4MNbMugTrLgZmF3JfIsUitXkt3rrlDKonxHHVv77h/TkbCt5IpAKJVohMAIaZ2SjgCmC+mT2Yq81DwBhgB1ALGAfcD4wF0oFp7j6JyGWvbmb2OHBn0E6kxLSoU5W3bjmDzo1qMOKV73j6i2UauSUSiNqTDc0sGTgX+NLdT2oubjNLBH4KfOfuy4/Xtqw92VBKr30HD/O7N+bwn9nrufq0ptz/Xx0qzHT6UvEU9smGUZsTw923cXSE1snuay/wRnHsS6SwEuJjeXxoV5okJ/LU5GWs27aXJ6/pTrXKmlpGKi79GiVyAmJijN8PbMdDQzoxdekWLn96Ght3aPJGqbgUIiJFcFWvpjz/856sydzDxU9+xYL1O8MuSSQUChGRIjq7bQqv39QHM7j86a/5fPHmsEsSiTqFiMhJOLVBdSaMOIPmdapyw4tpvPztqrBLEokqhYjISapXPYHxN/bh7LYp3P32PB76cGGhHiAmUh4oRESKQdXKcYwZ1oNhvZvxzBfL+fW4Wew7qMkbpfzT2ESRYhIXG8P9F3WgWe0q/OmDhWzYsZd/XZtK7WqVwy5NpMSoJyJSjMyMG/q25KmruzN//U6GjP6a5RlZYZclUmIUIiIl4IJODRg3vDdZ+w4xZPTXTF+RGXZJIiVCISJSQro3TebtW86gVtVK/OzZb3knfV3BG4mUMQoRkRLUtHYV3rr5dLo1rclvXk3nyc+XavJGKVcUIiIlrGaVSrz0y15c0q0Rf/14MXe+OZeDh4+EXZZIsdDoLJEoqBwXy6grutCkVhX+8ekS1u+ITN5YPSE+7NJETop6IiJRYmbcdm5b/npZZ6Yt28rlo6exYcfesMsSOSkKEZEouzy1CS9d34v12/fyixdmkLX/UNgliRSZQkQkBKe3rsPon/VgyeYsRo6bxWFNkyJlVNRCxMyeM7NpZnZPPu8nm9kHZpZmZs8E62qY2YdmNtHM3jazSmYWZ2arzWxy8NMpWucgUpzObFOH+/6rA58t2syf3l8YdjkiRXLCIWJmVc0s9gS3GQLEunsfoKWZtcmj2TDg5eBxjElmlgpcA4xy9/OAjcBAoDMwzt37BT9zT/QcREqLn/VuxvVntOD5r1bwf99oBmApewoMETOLMbOrzex9M9sMLAI2mNl8M/trPoGQWz+OPhp3InBmHm22Ah3NrCbQBFjj7k+5+yfB+ynAZqA3MNjMpge9m2NGmJnZ8KBHk5aRkVGI8kTCc/dPT+WcdnW59935TF2yJexyRE5IYXoinwOtgLuA+u7exN3rAn2Bb4C/mNnPCthHVSD767qZQL082kwFmgEjgYVBOwDMrA+Q7O7fADOAAe7eC4gHBuXekbuPcfdUd09NSUkpxCmKhCc2xvjHVd1oU7caN788k6WbNdeWlB2FCZEB7v6Au89x9x++IeXume7+prtfCrxWwD6ygMRguVo+x70XuMnd7yfS2/kFgJnVAp4Arg/azXH3DcFyGlCYnpBIqVatchzPXpdK5bgYfvniDDJ3Hwi7JJFCKTBE3P0ggJk9mPu97Hsj2W2OYyZHL2F1AVbm0SYZ6BTs8zTAzawS8Dpwl7tnXzAea2ZdgnYXA7MLOgeRsqBxchXGXJvKhh37uGnsTPYf0vNIpPQ7kRvrjczsquwXZlYXmFTIbScAw8xsFHAFMD+PUHoIGAPsAGoB44BfAt2Bu4ORWEOB+4GxQDowzd0LW4NIqde9aTKPXd6F6Ssz+Z+35mmeLSn1TmTakxuBj81sGeDAC8AdhdnQ3XeaWT/gXOARd99Irh6Eu08HOuTadHTwk1vnE6hbpEy5sEtDlmfs5m+TvqdV3arc0q912CWJ5KvAEDGzl4DvgFnACOAV4BBwsbsvLeyB3H0bR0doichxjPxJa5ZlZPHIR4tpWacqAzs2CLskkTwV5nLWi0G764kESHNgG/AzM7us5EoTqbjMjEcu60z3pjW59bV05q7dEXZJInkqzI31T919lLtf5+5dgTrA7cAyIt/ZEJESkBAfyzPDUqldtTI3vDSDjTv2hV2SyDEK82VDy/na3Q8Fw33Huvtv82ojIsUjJakyz/+8J7v3H+aXL85gzwFN1iilS6G+bGhmvzazpjlXBvNYnWNmLwLXlUx5InJK/SSeuKobCzfs5NZX0zmiyRqlFClMiAwEDgPjzGy9mS0wsxXAEuAq4G/u/u8SrFGkwuvfri5/GNyeiQs28cjHi8MuR+QHhRniWwWY4O5PmVk8kXsie919e8mWJiI5/fz05izLyOLpL5bRMqUqV6Q2CbskkUL1RB4luFwVfDP9TWCMmd1pZo1KsjgROcrM+N8LO9C3TR3ufnsu3yzfGnZJIoUKkR7AX3K8TgKeI9IjuaskihKRvMXFxvDPq7vTrHZVbvq/mazYsjvskqSCK0yI7Pcfz73wmbt/DPwOSC2ZskQkPzUS43n+up4Y8Mt/z2DHnoKmrhMpOYUJkX1m1iz7hbv/JvjTiUzFLiJR1rR2ZLLGtdv2cvPLMzl4+EjBG4mUgMKEyJ+ACWbWLudKM2vAic29JSLFqGfzWjw0pBNfL9vKH9+Zr8kaJRQFhoC7f2xm1Yl8XyQdmBe8NQTI83npIhIdl/ZozPItWTz5+TJapVTlhr4twy5JKphC9STc/XUze5/IUwQ7AHuBIe6uZ3mIhOz2c09hecZu/vTBQprXrsqA9nk9OFSkZBT6eSLuvsfd33D3+9z9EQWISOkQE2OMuqIrHRvWYOSrs1iwfmfYJUkFciIPpRKRUiqxUizPXpdKjcR4bnhxBpt3abJGiY6ohYiZPWdm08wsz/soZpZsZh+YWZqZPXO87Qral0hFVK96As9el8r2vQf51Usz2XdQj9eVkheVEDGzIUCsu/cBWppZmzyaDQNedvdUIMnMUvParpD7EqmQOjSswd+HdmXO2u3cPn62JmuUEhetnkg/jj7VcCJwZh5ttgIdzawm0ARYk892Be7LzIYHPZq0jIyM4jkDkTLivA71ueuCdrw/dwN/n/R92OVIORetEKkKrAuWM4G8ho9MBZoBI4GFQbu8titwX+4+xt1T3T01JSWluM5BpMz4Vd+WDE1twj8+W8qEWesK3kCkiKL1ZcEsIDFYrkbe4XUvcJO77zSz24Bf5LNdYfYlUqGZGQ9c3JFVmbv5/RtzaJycSGrzWmGXJeVQtD6AZ3L0slMXYGUebZKBTmYWC5wGeD7bFWZfIhVepbgYnv5ZDxolJ3Lj2JmsydwTdklSDkUrRCYAw8xsFHAFMN/MHszV5iFgDLADqAWMy2O79/NZJyJ5qFmlEs9dl8qhI871/57Bzn2arFGKV1RCxN13Erkh/g3Q391nu/s9udpMd/cO7l7N3c9196w8ttuR17ponINIWdUypRqjr+nOii27+fUrszikyRqlGEXtfoK7b3P38e6+8WS3K+q+RCqq01vX4cGLO/LF9xk88N6CsMuRckSz8IpUEFf2asryLbsZ8+VyWqZU47rTm4ddkpQDChGRCuSOge1YnrGb+/4zn2a1q9DvlLphlyRlnIbHilQgsTHG41d25ZT61fn1K7P4ftOusEuSMk4hIlLBVK0cx3PXpZJQKZbr/z2DrVn7wy5JyjCFiEgF1LBmIs9em0rGrv0MH6vJGqXoFCIiFVSXJjUZdUVXZq7axl1vzdXjdaVIFCIiFdhPOzfgt+e15e1Z63jy86VhlyNlkEZniVRwI/q3ZlnGbh6d+D3N61RlcOeGYZckZYh6IiIVnJnxl0s7kdosmdvHzyZ9zfawS5IyRCEiIlSOi+WZYT2oW70yN7yYxkfzNjB7zXY27tinaVLkuKy830xLTU31tLS0sMsQKROWbNrFZU9PY8feoxM1mkGdapWpV70y9ZISqFs9IbIc/Fk3KYH6NRKoVaUSMTEWYvVSnMxsZvCk2ePSPRER+UGbeklMvaM/K7fsYdPOfWzatY9NO/fkG3a4AAAQXklEQVSzeec+Nu3cx4Yd+5i9djtbsg4cs21cjFE3qXKukEmgbtLR5XrVK1MjMR4zhU15oRARkR9JSoinU+MadKJGvm0OHDrClqz9kaDZuZ/NuyIhs3FHZHnFlt18szzzRz2abJXiYn7o1dSrkRD5MwidujnCp1plfTyVBfpXEpETVikuhoY1E2lYM/G47fYdPMzmnfuDHs2PezWbdu5n4YadfLE4g6z9h47Ztmql2B8FS/3qCQzt2YSWKdVK6rSkCBQiIlJiEuJjaVq7Ck1rVzluu6z9h4Jg2RcJnSBkNu3ax+ad+5i1ejsbduzlg3kbeH9kX6onxEfpDKQgChERCV21ynFUS6lGq+P0Mmau2sYVz0zjDxPm8fehXXVfpZSI2hBfM3vOzKaZ2T35vH+zmU0OftLN7Jl81sWZ2eoc6ztF6xxEJDw9miXz3wPa8E76et76bl3Y5UggKiFiZkOAWHfvA7Q0sza527j7aHfv5+79gCnAv/JaB3QGxmWvd/e50TgHEQnfzf1a07tlLf74zjxWbtkddjlC9Hoi/YDxwfJE4Mz8GppZI6Ceu6fls643MNjMpge9m2MuyZnZcDNLM7O0jIyM4jwPEQlRbIzxt6FdiY+LYeSrszhwSF+EDFu0QqQqkN3/zATqHaftCGD0cdbNAAa4ey8gHhiUewfuPsbdU909NSUl5aQKF5HSpUGNRB6+tDNz1u7gsU8Wh11OhRetEMkCsscCVsvvuGYWA/QHJh9n3Rx33xAspwHHXBoTkfLt/A71uea0pjzzxXKmLtkSdjkVWrRCZCZHL2F1AVbm064v8K3/eC6W3OvGmlkXM4sFLgZml0C9IlLK3fPT9rSpW43/Hp+upzOGKFohMgEYZmajgCuA+Wb2YB7tzge+LGDd/cBYIB2Y5u6TSqBeESnlEivF8sTV3dix9yC/e2OOHqoVkqhNwGhmycC5wJfuvjEqB0UTMIqUdy9+vZJ7353PvRe25xdntAi7nHKjsBMwRu17Iu6+zd3HRzNARKT8u7ZPMwacWpeHPljEgvU7wy6nwtHzRESkTDMzHrmsCzWrxPPrcd+x98DhsEuqUBQiIlLm1apaib8N7cryLbu5/70FYZdToShERKRcOKN1HW48qxXjpq/mo3kbCt5AioVCRETKjdvPa0uXxjW44825rN++N+xyKgSFiIiUG/GxMfzjqm4cOnyEW19L5/ARDfstaQoRESlXmtWuygMXd2T6ikye/Hxp2OWUewoRESl3hnRvzCXdGvH4p0uYuSoz7HLKNYWIiJRL91/UgUY1Exk5Lj3PZ71L8VCIiEi5lJQQzz+u6samnfu4++25mhalhChERKTc6tqkJred15b35mzg9bS1YZdTLilERKRcu+msVpzeqjb3vjufZRlZYZdT7ihERKRciwmehpgQH8PIcbPYf0jTohQnhYiIlHv1qifw18u6MH/9Tv76kZ6GWJwUIiJSIQxoX49r+zTj2akrmLx4c9jllBsKERGpMP5n0KmcUi+J374+m4xdehpicVCIiEiFkRAfeRrirn2H+O3rszmiaVFOWtRCxMyeM7NpZnZPPu/fbGaTg590M3vGzOLMbHWO9Z2CtveZ2QwzezJa9YtI+dC2XhL3DG7PF99n8PxXK8Iup8yLSoiY2RAg1t37AC3NrE3uNu4+2t37uXs/YArwL6AzMC57vbvPNbMewJlAL2CzmQ2IxjmISPnxs9Oacl77ejz80SLmrdsRdjllWrR6Iv2A8cHyRCIhkCczawTUc/c0oDcw2MymBz2ZOOBs4E2PfP30Y6BvHvsYbmZpZpaWkZFRzKciImWdmfHwpZ2pXbUyI1+dxZ4Dh8IuqcyKVohUBdYFy5lAveO0HQGMDpZnAAPcvRcQDwwqzL7cfYy7p7p7akpKSjGULyLlTXLVSowa2oUVW3Zz37t6GmJRRStEsoDEYLlafsc1sxigPzA5WDXH3bMfUZYGtCnsvkRECnJ6qzrc0q8Vr6Wt4b0568Mup0yK1gfwTI5ewuoCrMynXV/gWz86U9pYM+tiZrHAxcDsE9iXiEiBbh3Qlq5NanLXW3NZk7kn7HLKnGiFyARgmJmNAq4A5pvZg3m0Ox/4Msfr+4GxQDowzd0nAVOBbmb2OHAnMK5EKxeRci0+NoZ/XNkNd7j1tXQOHT4SdkllikVremQzSwbOBb50940nua9E4KfAd+6+/HhtU1NTPS0t7WQOJyIVwDvp6/jNq+mM/Ekbbju3bdjlhM7MZrp7akHtonY/wd23ufv4kw2QYF973f2NggJERKSwLuraiEu7N+afny1h+go9DbGwdFNaRCRw30UdaFqrCre+Oosde/Q0xMJQiIiIBKpVjuMfV3UjI2s/d741R09DLASFiIhIDp0b1+S3553Ch/M28uqMNWGXU+opREREcvlV35b0bVOH+/4zn6Wbd4VdTqmmEBERySUmxnjs8i5UqRTHr8els++gnoaYH4WIiEge6lZP4NHLO7Nww04e/mhR2OWUWgoREZF8nNOuHj8/vTkvfLWSzxfpaYh5UYiIiBzHnRe049QG1fnt67PZvHNf2OWUOgoREZHjSIiP5YmrurL7wCFuG6+nIeamEBERKUDrukn8cXAHpi7dwr+maKKMnBQiIiKFcFWvJgzsUJ+/fryYOWu3h11OqaEQEREpBDPjL5d2IiWpMiPHzSJrv56GCAoREZFCq1mlEn8f2pXVmXu49535YZdTKihEREROwGkta/P/+rfmze/W8k76uoI3KOcUIiIiJ2jkT9rQo1ky97w9r8I/DTFqIWJmz5nZNDO7J5/3bzazycFPupk9Y2Y1zOxDM5toZm+bWSUzizOz1TnadorWOYiIAMTFxvD4lV3BYOSrszhYgZ+GGJUQMbMhQKy79wFamlmb3G3cfbS793P3fsAU4F/ANcAodz8P2AgMBDoD47LbuvvcaJyDiEhOjZOr8NCQTsxavZ3Lnp7GYxMX8+X3GRXuhntclI7TDxgfLE8EzgSW5NXQzBoB9dw9Dcj5XNsUYDPQGxhsZv2BucCN7n4o1z6GA8MBmjZtWnxnISKSw+DODdm8cz8T0tfx1ORlHD6ylBiD9g2r07N5LXo1r0Vq81qkJFUOu9QSE60QqQpk34HKBLofp+0IYHTOFWbWB0h292/M7DAwwN03mNlLwCDg3Zzt3X0MMAYiz1gvnlMQETnW9We24PozW5C1/xCzVm9jxopMpq/M5JVvV/PCVysBaFmnKj2b1yK1eTK9WtSiaa0qmFm4hReTaIVIFpAYLFcjn8toZhYD9AfuzrGuFvAEcGmwao677w+W04BjLo2JiERbtcpx9G2TQt82KQAcOHSEuet2MGNlJmkrM/lo/kZeS4s85KpuUmV6toj0VHo2r8Up9ZOIjSmboRKtEJlJ5BLWN0AXYHE+7foC33rwTEozqwS8Dtzl7quCNmPN7E/APOBi4M8lWbiISFFUiouhR7NkejRLhrNbceSIs2RzFtNXZjJjRSYzVmby/pwNACQlxJHaLJmeLSKh0rlxDSrHxYZ8BoVj0XiGsJlVJ3Kz/FPgAuBK4HJ3vydXuz8Dae7+VvD6ZiIhMTtoMhqYD7wCGPCuu9/NcaSmpnpaWtrxmoiIRJ27s3bbXtJWZTJ9xTZmrMxk6eYsIBJAXRvXpGeLZHo2r0WPZskkJcRHtT4zm+nuqQW2i9aD6M0sGTgX+NLdN0bloChERKTsyNx9gBnZPZVV25i3bgeHjzgxBu3qV6dX0FPp2SKZukkJJVpLqQuRsChERKSs2nPgELNWb2d6cPlr1urt7A0e1du8dpUgUCLB0rx28d6sL2yIROueiIiInKAqleI4o3UdzmhdB4CDh48wL7hZP2PlNiYt3MTrM9cCkJJUmZ7NI5e/ejavxakNqkflZr16IiIiZdSRI86yjJw367exbvteIDJa7MqeTbhncPsi7Vs9ERGRci4mxmhTL4k29ZK45rRmAKzbvpe0lZlMX5FJw5qJBezh5ClERETKkUY1E2nUtREXdW0UleNpFl8RESkyhYiIiBSZQkRERIpMISIiIkWmEBERkSJTiIiISJEpREREpMgUIiIiUmTlftoTM8sAVhXYMH91gC3FVE5xUl0nRnWdGNV1YspjXc3cPaWgRuU+RE6WmaUVZv6YaFNdJ0Z1nRjVdWIqcl26nCUiIkWmEBERkSJTiBRsTNgF5EN1nRjVdWJU14mpsHXpnoiIiBSZeiIiIlJkChEpNmZWy8zONbM6YdciItGhEDkOM6tnZlPCriObmdUwsw/NbKKZvW1mlcKuKZuZJQPvAb2Az82swPHl0RL8O84Ku45sZhZnZqvNbHLw0ynsmnIzs6fM7MKw68hmZjfn+PtKN7Nnwq4JIv/dm9kHZpZWimpqYWbvm9kUM3uspI+nEMlH8KH4IlA17FpyuAYY5e7nARuBgSHXk1Nn4DZ3/xPwMdA95HpyehQo+eeEFl5nYJy79wt+5oZdUE5m1heo7+7/CbuWbO4+OvvvC5gC/CvkkrINA14OvouRZGal4bsiDwMPuHtfoLGZ9SvJgylE8ncYGArsDLuQbO7+lLt/ErxMATaHWU9O7v6Fu39jZmcR6Y1MC7smADM7B9hNJHRLi97AYDObbmbPmVmpeUy1mcUT+YBeaWYXhV1PbmbWCKjn7mlh1xLYCnQ0s5pAE2BNyPUAtAW+C5Y3AzVK8mAKkXy4+0533xF2HXkxsz5Asrt/E3YtOZmZEQnebcDBkMshuNz3B+DOsGvJZQYwwN17AfHAoJDryelaYAHwCNDLzH4dcj25jQBGh11EDlOBZsBIYCGQGW45ALwB3BtcjhwIfFqSB1OIlDFmVgt4Arg+7Fpy84gRwBzgv8Kuh0h4POXu28MuJJc57r4hWE4D2oRZTC7dgDHuvhH4P6B/yPX8wMxiiNQzOeRScroXuMnd7wcWAb8IuR7c/UHgQ+AG4EV3zyrJ4ylEypDgN+vXgbvc/WQmlSx2ZnaHmV0bvKwJlIYP7gHACDObDHQ1s2dDrifbWDPrYmaxwMXA7LALymEp0DJYTuXkJi8tbn2Bb710fbktGegU/FueBpSW2tKBpsCokj6QvmxYADObHNzMC52Z3Qz8maMfOqPd/bUQS/pBMBBhPFAZmAeMKE3/s5eyf8eOwCuAAe+6+90hl/QDM0sCngfqEbnUdpm7rwu3qggz+zOQ5u5vhV1LNjPrBbxA5JLWNOCSkv7NvzDM7D5gqbuPLfFjlaL/z0VEpIzR5SwRESkyhYiIiBSZQkRERIpMISIiIkWmEBERkSJTiIiISJEpRESizMxuNLOng+V4MxtrZi8G81aJlCkKEZHo6wzMMbPqRKanWO3u17l76PONiZwohYhI9HUiMlHfZOD10vSNdZETpW+si0SZmW0DDgHXl6ZndogURal5joFIRWBmTYAsYAnQIORyRE6aQkQkujoTmUDzV8A3ZjbD3UvNo3tFTpTuiYhEVydgbvA8kRuA18ysRJ88J1KSFCIi0dUJmAsQPOp4PJGp10XKJN1YFxGRIlNPREREikwhIiIiRaYQERGRIlOIiIhIkSlERESkyBQiIiJSZAoREREpsv8P25AOs5eHdO4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal choice of k is 2\n"
     ]
    }
   ],
   "source": [
    "#### (c)\n",
    "#计算Gk\n",
    "Gk = np.log(Ein_rand) - np.log(Ein)\n",
    "\n",
    "#作图\n",
    "plt.plot(K, Gk)\n",
    "plt.title(\"$K$ VS $G(k)$\")\n",
    "plt.xlabel(\"$K$\")\n",
    "plt.ylabel(\"$G(k)$\")\n",
    "plt.show()\n",
    "\n",
    "#最优解\n",
    "k_opt = K[np.argmin(np.diff(Gk)) + 1]\n",
    "print(\"Optimal choice of k is {}\".format(k_opt))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### (d)\n",
    "#试验次数\n",
    "N = 100\n",
    "Sigma = [0.1, 0.3, 0.5, 0.75, 1]\n",
    "K_opt = []\n",
    "\n",
    "for sigma in Sigma:\n",
    "    #记录结果\n",
    "    Ein_rand_sigma = []\n",
    "    for k in K:\n",
    "        ein_k = []\n",
    "        for _ in range(N):\n",
    "            X, y = hlp.Data(n, scale=sigma) \n",
    "            #计算范围\n",
    "            X1_min = np.min(X[:, 0])\n",
    "            X1_max = np.max(X[:, 0])\n",
    "            X2_min = np.min(X[:, 1])\n",
    "            X2_max = np.max(X[:, 1])\n",
    "            #生成点\n",
    "            X1_rand = np.random.uniform(X1_min, X1_max, size=n)\n",
    "            X2_rand = np.random.uniform(X2_min, X2_max, size=n)\n",
    "            #合并\n",
    "            Xrand = np.c_[X1_rand, X2_rand]\n",
    "            #训练模型\n",
    "            kmeans = hlp.KMeans_(k)\n",
    "            kmeans.fit(Xrand)\n",
    "            #获得标签\n",
    "            label = kmeans.labels_\n",
    "            #获得聚类中心\n",
    "            center = kmeans.cluster_centers_\n",
    "            #计算Ein\n",
    "            ein = 0\n",
    "            for i in range(k):\n",
    "                #计算每一类的误差\n",
    "                ein += np.sum((Xrand[label==i] - center[i]) ** 2)\n",
    "            #计算均值\n",
    "            ein /= n\n",
    "            #存储结果\n",
    "            ein_k.append(ein)\n",
    "        Ein_rand_sigma.append(np.mean(ein_k))\n",
    "    Gk = np.log(Ein_rand_sigma) - np.log(Ein)\n",
    "    #记录最优k\n",
    "    k_opt = K[np.argmin(np.diff(Gk)) + 1]\n",
    "    K_opt.append(k_opt)\n",
    "\n",
    "#作图\n",
    "plt.plot(Sigma, K_opt)\n",
    "plt.title(\"$\\sigma$ VS $k$\")\n",
    "plt.xlabel(\"$\\sigma$\")\n",
    "plt.ylabel(\"$k$\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
